Dynamical Zeta Functions And Dynamical Determinants For Hyperbolic Maps

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Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps

Author : Viviane Baladi
Publisher : Springer
ISBN 13 : 3319776614
Total Pages : 296 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps by : Viviane Baladi

Download or read book Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps written by Viviane Baladi and published by Springer. This book was released on 2018-05-09 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The spectra of transfer operators associated to dynamical systems, when acting on suitable Banach spaces, contain key information about the ergodic properties of the systems. Focusing on expanding and hyperbolic maps, this book gives a self-contained account on the relation between zeroes of dynamical determinants, poles of dynamical zeta functions, and the discrete spectra of the transfer operators. In the hyperbolic case, the first key step consists in constructing a suitable Banach space of anisotropic distributions. The first part of the book is devoted to the easier case of expanding endomorphisms, showing how the (isotropic) function spaces relevant there can be studied via Paley–Littlewood decompositions, and allowing easier access to the construction of the anisotropic spaces which is performed in the second part. This is the first book describing the use of anisotropic spaces in dynamics. Aimed at researchers and graduate students, it presents results and techniques developed since the beginning of the twenty-first century.

Thermodynamic Formalism

Author : Mark Pollicott
Publisher : Springer Nature
ISBN 13 : 3030748634
Total Pages : 536 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Thermodynamic Formalism by : Mark Pollicott

Download or read book Thermodynamic Formalism written by Mark Pollicott and published by Springer Nature. This book was released on 2021-10-01 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume arose from a semester at CIRM-Luminy on “Thermodynamic Formalism: Applications to Probability, Geometry and Fractals” which brought together leading experts in the area to discuss topical problems and recent progress. It includes a number of surveys intended to make the field more accessible to younger mathematicians and scientists wishing to learn more about the area. Thermodynamic formalism has been a powerful tool in ergodic theory and dynamical system and its applications to other topics, particularly Riemannian geometry (especially in negative curvature), statistical properties of dynamical systems and fractal geometry. This work will be of value both to graduate students and more senior researchers interested in either learning about the main ideas and themes in thermodynamic formalism, and research themes which are at forefront of research in this area.

Cohomological Theory of Dynamical Zeta Functions

Author : Andreas Juhl
Publisher : Birkhäuser
ISBN 13 : 3034883404
Total Pages : 712 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Cohomological Theory of Dynamical Zeta Functions by : Andreas Juhl

Download or read book Cohomological Theory of Dynamical Zeta Functions written by Andreas Juhl and published by Birkhäuser. This book was released on 2012-12-06 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical zeta functions are associated to dynamical systems with a countable set of periodic orbits. The dynamical zeta functions of the geodesic flow of lo cally symmetric spaces of rank one are known also as the generalized Selberg zeta functions. The present book is concerned with these zeta functions from a cohomological point of view. Originally, the Selberg zeta function appeared in the spectral theory of automorphic forms and were suggested by an analogy between Weil's explicit formula for the Riemann zeta function and Selberg's trace formula ([261]). The purpose of the cohomological theory is to understand the analytical properties of the zeta functions on the basis of suitable analogs of the Lefschetz fixed point formula in which periodic orbits of the geodesic flow take the place of fixed points. This approach is parallel to Weil's idea to analyze the zeta functions of pro jective algebraic varieties over finite fields on the basis of suitable versions of the Lefschetz fixed point formula. The Lefschetz formula formalism shows that the divisors of the rational Hassc-Wcil zeta functions are determined by the spectra of Frobenius operators on l-adic cohomology.

Positive Transfer Operators And Decay Of Correlations

Author : Viviane Baladi
Publisher : World Scientific
ISBN 13 : 9814496669
Total Pages : 326 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Positive Transfer Operators And Decay Of Correlations by : Viviane Baladi

Download or read book Positive Transfer Operators And Decay Of Correlations written by Viviane Baladi and published by World Scientific. This book was released on 2000-07-12 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although individual orbits of chaotic dynamical systems are by definition unpredictable, the average behavior of typical trajectories can often be given a precise statistical description. Indeed, there often exist ergodic invariant measures with special additional features. For a given invariant measure, and a class of observables, the correlation functions tell whether (and how fast) the system “mixes”, i.e. “forgets” its initial conditions.This book, addressed to mathematicians and mathematical (or mathematically inclined) physicists, shows how the powerful technology of transfer operators, imported from statistical physics, has been used recently to construct relevant invariant measures, and to study the speed of decay of their correlation functions, for many chaotic systems. Links with dynamical zeta functions are explained.The book is intended for graduate students or researchers entering the field, and the technical prerequisites have been kept to a minimum.

Geometric and Probabilistic Structures in Dynamics

Author : Keith Burns
Publisher : American Mathematical Soc.
ISBN 13 : 0821842862
Total Pages : 358 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric and Probabilistic Structures in Dynamics by : Keith Burns

Download or read book Geometric and Probabilistic Structures in Dynamics written by Keith Burns and published by American Mathematical Soc.. This book was released on 2008 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book presents a collection of articles that cover areas of mathematics related to dynamical systems. The authors are well-known experts who use geometric and probabilistic methods to study interesting problems in the theory of dynamical systems and its applications. Some of the articles are surveys while others are original contributions. The topics covered include: Riemannian geometry, models in mathematical physics and mathematical biology, symbolic dynamics, random and stochastic dynamics. This book can be used by graduate students and researchers in dynamical systems and its applications."--BOOK JACKET.

Arithmetic L-Functions and Differential Geometric Methods

Author : Pierre Charollois
Publisher : Springer Nature
ISBN 13 : 3030652033
Total Pages : 324 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Arithmetic L-Functions and Differential Geometric Methods by : Pierre Charollois

Download or read book Arithmetic L-Functions and Differential Geometric Methods written by Pierre Charollois and published by Springer Nature. This book was released on 2021-05-17 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an outgrowth of the conference “Regulators IV: An International Conference on Arithmetic L-functions and Differential Geometric Methods” that was held in Paris in May 2016. Gathering contributions by leading experts in the field ranging from original surveys to pure research articles, this volume provides comprehensive coverage of the front most developments in the field of regulator maps. Key topics covered are: • Additive polylogarithms • Analytic torsions • Chabauty-Kim theory • Local Grothendieck-Riemann-Roch theorems • Periods • Syntomic regulator The book contains contributions by M. Asakura, J. Balakrishnan, A. Besser, A. Best, F. Bianchi, O. Gregory, A. Langer, B. Lawrence, X. Ma, S. Müller, N. Otsubo, J. Raimbault, W. Raskin, D. Rössler, S. Shen, N. Triantafi llou, S. Ünver and J. Vonk.

Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval

Author : David Ruelle
Publisher : American Mathematical Soc.
ISBN 13 : 9780821836019
Total Pages : 76 pages
Book Rating : 4.8/5 (36 download)

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Book Synopsis Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval by : David Ruelle

Download or read book Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval written by David Ruelle and published by American Mathematical Soc.. This book was released on 1994 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a general introduction to the subject, this title presents a detailed study of the zeta functions associated with piecewise monotone maps of the interval $ 0,1]$. In particular, it gives a proof of a generalized form of the Baladi-Keller theorem relating the poles of $\zeta (z)$ and the eigenvalues of the transfer operator.

Classical Nonintegrability, Quantum Chaos

Author : Andreas Knauf
Publisher : Birkhäuser
ISBN 13 : 3034889321
Total Pages : 104 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Classical Nonintegrability, Quantum Chaos by : Andreas Knauf

Download or read book Classical Nonintegrability, Quantum Chaos written by Andreas Knauf and published by Birkhäuser. This book was released on 2012-12-06 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos' intended to introduce students and beginning researchers to the techniques applied in nonin tegrable classical and quantum dynamics. Several of these lectures are collected in this volume. The basic phenomenon of nonlinear dynamics is mixing in phase space, lead ing to a positive dynamical entropy and a loss of information about the initial state. The nonlinear motion in phase space gives rise to a linear action on phase space functions which in the case of iterated maps is given by a so-called transfer operator. Good mixing rates lead to a spectral gap for this operator. Similar to the use made of the Riemann zeta function in the investigation of the prime numbers, dynamical zeta functions are now being applied in nonlinear dynamics. In Chapter 2 V. Baladi first introduces dynamical zeta functions and transfer operators, illustrating and motivating these notions with a simple one-dimensional dynamical system. Then she presents a commented list of useful references, helping the newcomer to enter smoothly into this fast-developing field of research. Chapter 3 on irregular scattering and Chapter 4 on quantum chaos by A. Knauf deal with solutions of the Hamilton and the Schr6dinger equation. Scatter ing by a potential force tends to be irregular if three or more scattering centres are present, and a typical phenomenon is the occurrence of a Cantor set of bounded orbits. The presence of this set influences those scattering orbits which come close.

Handbook of Dynamical Systems

Author : A. Katok
Publisher : Elsevier
ISBN 13 : 0080478220
Total Pages : 1235 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Handbook of Dynamical Systems by : A. Katok

Download or read book Handbook of Dynamical Systems written by A. Katok and published by Elsevier. This book was released on 2005-12-17 with total page 1235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second half of Volume 1 of this Handbook follows Volume 1A, which was published in 2002. The contents of these two tightly integrated parts taken together come close to a realization of the program formulated in the introductory survey "Principal Structures of Volume 1A.The present volume contains surveys on subjects in four areas of dynamical systems: Hyperbolic dynamics, parabolic dynamics, ergodic theory and infinite-dimensional dynamical systems (partial differential equations).. Written by experts in the field.. The coverage of ergodic theory in these two parts of Volume 1 is considerably more broad and thorough than that provided in other existing sources. . The final cluster of chapters discusses partial differential equations from the point of view of dynamical systems.

Smooth Ergodic Theory and Its Applications

Author : A. B. Katok
Publisher : American Mathematical Soc.
ISBN 13 : 0821826824
Total Pages : 895 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Smooth Ergodic Theory and Its Applications by : A. B. Katok

Download or read book Smooth Ergodic Theory and Its Applications written by A. B. Katok and published by American Mathematical Soc.. This book was released on 2001 with total page 895 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past decade, there have been several major new developments in smooth ergodic theory, which have attracted substantial interest to the field from mathematicians as well as scientists using dynamics in their work. In spite of the impressive literature, it has been extremely difficult for a student-or even an established mathematician who is not an expert in the area-to acquire a working knowledge of smooth ergodic theory and to learn how to use its tools. Accordingly, the AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications (Seattle, WA) had a strong educational component, including ten mini-courses on various aspects of the topic that were presented by leading experts in the field. This volume presents the proceedings of that conference. Smooth ergodic theory studies the statistical properties of differentiable dynamical systems, whose origin traces back to the seminal works of Poincare and later, many great mathematicians who made contributions to the development of the theory. The main topic of this volume, smooth ergodic theory, especially the theory of nonuniformly hyperbolic systems, provides the principle paradigm for the rigorous study of complicated or chaotic behavior in deterministic systems. This paradigm asserts that if a non-linear dynamical system exhibits sufficiently pronounced exponential behavior, then global properties of the system can be deduced from studying the linearized system. One can then obtain detailed information on topological properties (such as the growth of periodic orbits, topological entropy, and dimension of invariant sets including attractors), as well as statistical properties (such as the existence of invariant measures, asymptotic behavior of typical orbits, ergodicity, mixing, decay of corre This volume serves a two-fold purpose: first, it gives a useful gateway to smooth ergodic theory for students and nonspecialists, and second, it provides a state-of-the-art report on important current aspects of the subject. The book is divided into three parts: lecture notes consisting of three long expositions with proofs aimed to serve as a comprehensive and self-contained introduction to a particular area of smooth ergodic theory; thematic sections based on mini-courses or surveys held at the conference; and original contributions presented at the meeting or closely related to the topics that were discussed there.

Handbook of Dynamical Systems

Author : B. Hasselblatt
Publisher : Elsevier
ISBN 13 : 0080533442
Total Pages : 1231 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Dynamical Systems by : B. Hasselblatt

Download or read book Handbook of Dynamical Systems written by B. Hasselblatt and published by Elsevier. This book was released on 2002-08-20 with total page 1231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volumes 1A and 1B.These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample cross-references between individual surveys.The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics.Volume 1B will appear 2005.

Modern Dynamical Systems and Applications

Author : Michael Brin
Publisher : Cambridge University Press
ISBN 13 : 9780521840736
Total Pages : 490 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis Modern Dynamical Systems and Applications by : Michael Brin

Download or read book Modern Dynamical Systems and Applications written by Michael Brin and published by Cambridge University Press. This book was released on 2004-08-16 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a broad collection of current research by leading experts in the theory of dynamical systems.

European Congress of Mathematics

Author : Carles Casacuberta
Publisher : Birkhäuser
ISBN 13 : 3034882688
Total Pages : 611 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis European Congress of Mathematics by : Carles Casacuberta

Download or read book European Congress of Mathematics written by Carles Casacuberta and published by Birkhäuser. This book was released on 2012-12-06 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: R. Ahlswede, V. Bach, V. Baladi, J. Bruna, N. Burq, X. Cabré, P.J. Cameron, Z. Chatzidakis, C. Ciliberto, G. Dal Maso, J. Denef, R. Dijkgraaf, B. Fantechi, H. Föllmer, A.B. Goncharov, A. Grigor'yan, M. Harris, R. Iturriaga, K. Johansson, K. Khanin, P. Koskela, H.W. Lenstra, Jr., F. Loeser, Y.I. Manin, N.S. Manton, Y. Meyer, I. Moerdijk, E.M. Opdam, T. Peternell, B.M.A.G. Piette, A. Reznikov, H. Schlichtkrull, B. Schmidt, K. Schmidt, C. Simó, B. Tóth, E. van den Ban, M.-F. Vignéras, O. Viro.

Modeling, Dynamics, Optimization and Bioeconomics I

Author : Alberto Adrego Pinto
Publisher : Springer
ISBN 13 : 331904849X
Total Pages : 749 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Modeling, Dynamics, Optimization and Bioeconomics I by : Alberto Adrego Pinto

Download or read book Modeling, Dynamics, Optimization and Bioeconomics I written by Alberto Adrego Pinto and published by Springer. This book was released on 2014-06-20 with total page 749 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores the emerging and current, cutting-edge theories and methods of modeling, optimization, dynamics and bio economy. It provides an overview of the main issues, results and open questions in these fields as well as covers applications to biology, economy, energy, industry, physics, psychology and finance. The majority of the contributed papers for this volume come from the participants of the International Conference on Modeling, Optimization and Dynamics (ICMOD 2010), a satellite conference of EURO XXIV Lisbon 2010, which took place at Faculty of Sciences of University of Porto, Portugal and from the Berkeley Bio economy Conference 2012, at the University of California, Berkeley, USA.

Progress of Theoretical Physics

Author :
Publisher :
ISBN 13 :
Total Pages : 866 pages
Book Rating : 4.X/5 (6 download)

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Book Synopsis Progress of Theoretical Physics by :

Download or read book Progress of Theoretical Physics written by and published by . This book was released on 2003 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dynamics Beyond Uniform Hyperbolicity

Author : Christian Bonatti
Publisher : Springer Science & Business Media
ISBN 13 : 3540268448
Total Pages : 390 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Dynamics Beyond Uniform Hyperbolicity by : Christian Bonatti

Download or read book Dynamics Beyond Uniform Hyperbolicity written by Christian Bonatti and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is Dynamics about? In broad terms, the goal of Dynamics is to describe the long term evolution of systems for which an "infinitesimal" evolution rule is known. Examples and applications arise from all branches of science and technology, like physics, chemistry, economics, ecology, communications, biology, computer science, or meteorology, to mention just a few. These systems have in common the fact that each possible state may be described by a finite (or infinite) number of observable quantities, like position, velocity, temperature, concentration, population density, and the like. Thus, m the space of states (phase space) is a subset M of an Euclidean space M . Usually, there are some constraints between these quantities: for instance, for ideal gases pressure times volume must be proportional to temperature. Then the space M is often a manifold, an n-dimensional surface for some n

Quantum Chaos and Mesoscopic Systems

Author : N.E. Hurt
Publisher : Springer Science & Business Media
ISBN 13 : 9401587922
Total Pages : 350 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Quantum Chaos and Mesoscopic Systems by : N.E. Hurt

Download or read book Quantum Chaos and Mesoscopic Systems written by N.E. Hurt and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 4. 2 Variance of Quantum Matrix Elements. 125 4. 3 Berry's Trick and the Hyperbolic Case 126 4. 4 Nonhyperbolic Case . . . . . . . 128 4. 5 Random Matrix Theory . . . . . 128 4. 6 Baker's Map and Other Systems 129 4. 7 Appendix: Baker's Map . . . . . 129 5 Error Terms 133 5. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 133 5. 2 The Riemann Zeta Function in Periodic Orbit Theory 135 5. 3 Form Factor for Primes . . . . . . . . . . . . . . . . . 137 5. 4 Error Terms in Periodic Orbit Theory: Co-compact Case. 138 5. 5 Binary Quadratic Forms as a Model . . . . . . . . . . . . 139 6 Co-Finite Model for Quantum Chaology 141 6. 1 Introduction. . . . . . . . 141 6. 2 Co-finite Models . . . . . 141 6. 3 Geodesic Triangle Spaces 144 6. 4 L-Functions. . . . . . . . 145 6. 5 Zelditch's Prime Geodesic Theorem. 146 6. 6 Zelditch's Pseudo Differential Operators 147 6. 7 Weyl's Law Generalized 148 6. 8 Equidistribution Theory . . . . . . . . . 150 7 Landau Levels and L-Functions 153 7. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 153 7. 2 Landau Model: Mechanics on the Plane and Sphere. 153 7. 3 Landau Model: Mechanics on the Half-Plane 155 7. 4 Selberg's Spectral Theorem . . . . . . . . . . . 157 7. 5 Pseudo Billiards . . . . . . . . . . . . . . . . . 158 7. 6 Landau Levels on a Compact Riemann Surface 159 7. 7 Automorphic Forms . . . . . 160 7. 8 Maass-Selberg Trace Formula 162 7. 9 Degeneracy by Selberg. . . . 163 7. 10 Hecke Operators . . . . . . . 163 7. 11 Selberg Trace Formula for Hecke Operators 167 7. 12 Eigenvalue Statistics on X . . . . 169 7. 13 Mesoscopic Devices. . . . . . . . 170 7. 14 Hall Conductance on Leaky Tori 170 7.