Selberg Zeta Functions And Transfer Operators

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Selberg Zeta Functions and Transfer Operators

Author : Markus Szymon Fraczek
Publisher : Springer
ISBN 13 : 331951296X
Total Pages : 363 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Selberg Zeta Functions and Transfer Operators by : Markus Szymon Fraczek

Download or read book Selberg Zeta Functions and Transfer Operators written by Markus Szymon Fraczek and published by Springer. This book was released on 2017-05-11 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the discrete spectra and resonances of hyperbolic Laplacians under both singular and non-singular perturbations. Areas in which the theory has not yet been sufficiently developed, such as the spectral theory of transfer operators or the singular perturbation theory of hyperbolic Laplacians, will profit from the numerical experiments discussed in this book. Detailed descriptions of numerical approaches to the spectra and eigenfunctions of transfer operators and to computations of Selberg zeta functions will be of value to researchers active in analysis, while those researchers focusing more on numerical aspects will benefit from discussions of the analytic theory, in particular those concerning the transfer operator method and the spectral theory of hyperbolic spaces.

Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume

Author : Roelof Bruggeman
Publisher : American Mathematical Society
ISBN 13 : 1470465450
Total Pages : 186 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume by : Roelof Bruggeman

Download or read book Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume written by Roelof Bruggeman and published by American Mathematical Society. This book was released on 2023-07-31 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

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.

Dynamics and Numbers

Author : Sergiǐ Kolyada:
Publisher : American Mathematical Soc.
ISBN 13 : 1470420201
Total Pages : 330 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Dynamics and Numbers by : Sergiǐ Kolyada:

Download or read book Dynamics and Numbers written by Sergiǐ Kolyada: and published by American Mathematical Soc.. This book was released on 2016-07-27 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of survey and research articles from the special program and international conference on Dynamics and Numbers held at the Max-Planck Institute for Mathematics in Bonn, Germany in 2014. The papers reflect the great diversity and depth of the interaction between number theory and dynamical systems and geometry in particular. Topics covered in this volume include symbolic dynamics, Bratelli diagrams, geometry of laminations, entropy, Nielsen theory, recurrence, topology of the moduli space of interval maps, and specification properties.

Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology

Author : Jens Bölte
Publisher : Cambridge University Press
ISBN 13 : 1107610494
Total Pages : 285 pages
Book Rating : 4.1/5 (76 download)

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Book Synopsis Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology by : Jens Bölte

Download or read book Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology written by Jens Bölte and published by Cambridge University Press. This book was released on 2012 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leading experts introduce this classical subject with exciting new applications in theoretical physics.

Emerging Applications of Number Theory

Author : Dennis A. Hejhal
Publisher : Springer Science & Business Media
ISBN 13 : 1461215447
Total Pages : 693 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Emerging Applications of Number Theory by : Dennis A. Hejhal

Download or read book Emerging Applications of Number Theory written by Dennis A. Hejhal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity. The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications. Concentration was on number theory's recent links with: (a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and (b) graph theory (especially expander graphs and related spectral theory). This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.

Period Functions for Maass Wave Forms and Cohomology

Author : R. Bruggeman
Publisher : American Mathematical Soc.
ISBN 13 : 1470414074
Total Pages : 150 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Period Functions for Maass Wave Forms and Cohomology by : R. Bruggeman

Download or read book Period Functions for Maass Wave Forms and Cohomology written by R. Bruggeman and published by American Mathematical Soc.. This book was released on 2015-08-21 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors construct explicit isomorphisms between spaces of Maass wave forms and cohomology groups for discrete cofinite groups Γ⊂PSL2(R). In the case that Γ is the modular group PSL2(Z) this gives a cohomological framework for the results in Period functions for Maass wave forms. I, of J. Lewis and D. Zagier in Ann. Math. 153 (2001), 191-258, where a bijection was given between cuspidal Maass forms and period functions. The authors introduce the concepts of mixed parabolic cohomology group and semi-analytic vectors in principal series representation. This enables them to describe cohomology groups isomorphic to spaces of Maass cusp forms, spaces spanned by residues of Eisenstein series, and spaces of all Γ-invariant eigenfunctions of the Laplace operator. For spaces of Maass cusp forms the authors also describe isomorphisms to parabolic cohomology groups with smooth coefficients and standard cohomology groups with distribution coefficients. They use the latter correspondence to relate the Petersson scalar product to the cup product in cohomology.

Dynamical, Spectral, and Arithmetic Zeta Functions

Author : Michel Laurent Lapidus
Publisher : American Mathematical Soc.
ISBN 13 : 0821820796
Total Pages : 210 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Dynamical, Spectral, and Arithmetic Zeta Functions by : Michel Laurent Lapidus

Download or read book Dynamical, Spectral, and Arithmetic Zeta Functions written by Michel Laurent Lapidus and published by American Mathematical Soc.. This book was released on 2001 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The original zeta function was studied by Riemann as part of his investigation of the distribution of prime numbers. Other sorts of zeta functions were defined for number-theoretic purposes, such as the study of primes in arithmetic progressions. This led to the development of $L$-functions, which now have several guises. It eventually became clear that the basic construction used for number-theoretic zeta functions can also be used in other settings, such as dynamics, geometry, and spectral theory, with remarkable results. This volume grew out of the special session on dynamical, spectral, and arithmetic zeta functions held at the annual meeting of the American Mathematical Society in San Antonio, but also includes four articles that were invited to be part of the collection. The purpose of the meeting was to bring together leading researchers, to find links and analogies between their fields, and to explore new methods. The papers discuss dynamical systems, spectral geometry on hyperbolic manifolds, trace formulas in geometry and in arithmetic, as well as computational work on the Riemann zeta function. Each article employs techniques of zeta functions. The book unifies the application of these techniques in spectral geometry, fractal geometry, and number theory. It is a comprehensive volume, offering up-to-date research. It should be useful to both graduate students and confirmed researchers.

Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

Author : Bernold Fiedler
Publisher : Springer Science & Business Media
ISBN 13 : 3642565891
Total Pages : 816 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems by : Bernold Fiedler

Download or read book Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems written by Bernold Fiedler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.

On the Theory of Maass Wave Forms

Author : Tobias Mühlenbruch
Publisher : Springer Nature
ISBN 13 : 3030404757
Total Pages : 527 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis On the Theory of Maass Wave Forms by : Tobias Mühlenbruch

Download or read book On the Theory of Maass Wave Forms written by Tobias Mühlenbruch and published by Springer Nature. This book was released on 2020-05-06 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a rigorous analytical treatment of the theory of Maass wave forms. Readers will find this unified presentation invaluable, as it treats Maass wave forms as the central area of interest. Subjects at the cutting edge of research are explored in depth, such as Maass wave forms of real weight and the cohomology attached to Maass wave forms and transfer operators. Because Maass wave forms are given a deep exploration, this book offers an indispensable resource for those entering the field. Early chapters present a brief introduction to the theory of classical modular forms, with an emphasis on objects and results necessary to fully understand later material. Chapters 4 and 5 contain the book’s main focus: L-functions and period functions associated with families of Maass wave forms. Other topics include Maass wave forms of real weight, Maass cusp forms, and weak harmonic Maass wave forms. Engaging exercises appear throughout the book, with solutions available online. On the Theory of Maass Wave Forms is ideal for graduate students and researchers entering the area. Readers in mathematical physics and other related disciplines will find this a useful reference as well. Knowledge of complex analysis, real analysis, and abstract algebra is required.

Algebraic and Topological Dynamics

Author : S. F. Koli︠a︡da
Publisher : American Mathematical Soc.
ISBN 13 : 0821837516
Total Pages : 378 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic and Topological Dynamics by : S. F. Koli︠a︡da

Download or read book Algebraic and Topological Dynamics written by S. F. Koli︠a︡da and published by American Mathematical Soc.. This book was released on 2005 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of articles from the special program on algebraic and topological dynamics and a workshop on dynamical systems held at the Max-Planck Institute (Bonn, Germany). It reflects the extraordinary vitality of dynamical systems in its interaction with a broad range of mathematical subjects. Topics covered in the book include asymptotic geometric analysis, transformation groups, arithmetic dynamics, complex dynamics, symbolic dynamics, statisticalproperties of dynamical systems, and the theory of entropy and chaos. The book is suitable for graduate students and researchers interested in dynamical systems.

From Phase Transitions To Chaos: Topics In Modern Statistical Physics

Author : G Gyorgyi
Publisher : World Scientific
ISBN 13 : 981450565X
Total Pages : 602 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis From Phase Transitions To Chaos: Topics In Modern Statistical Physics by : G Gyorgyi

Download or read book From Phase Transitions To Chaos: Topics In Modern Statistical Physics written by G Gyorgyi and published by World Scientific. This book was released on 1992-04-29 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises about forty research papers and essays covering a wide range of subjects in the forefront of contemporary statistical physics. The contributors are renown scientists and leading authorities in several different fields. This book is dedicated to Péter Szépfalusy on the occasion of his sixtieth birthday. Emphasis is placed on his two main areas of research, namely phase transitions and chaotic dynamical systems, as they share common aspects like the applicability of the probabilistic approach or scaling behaviour and universality. Several papers deal with equilibrium phase transitions, critical dynamics, and pattern formation. Also represented are disordered systems, random field systems, growth processes, and neural network. Statistical properties of interacting electron gases, such as the Kondo lattice, the Wigner crystal, and the Hubbard model, are treated. In the field of chaos, Hamiltonian transport and resonances, strange attractors, multifractal characteristics of chaos, and the effect of weak perturbations are discussed. A separate section is devoted to selected mathematical aspects of dynamical systems like the foundation of statistical mechanics, including the problem of ergodicity, and rigorous results on quantum chaos.

Issues in Algebra, Geometry, and Topology: 2013 Edition

Author :
Publisher : ScholarlyEditions
ISBN 13 : 1490105824
Total Pages : 700 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Issues in Algebra, Geometry, and Topology: 2013 Edition by :

Download or read book Issues in Algebra, Geometry, and Topology: 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-06-20 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Algebra, Geometry, and Topology / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Topology. The editors have built Issues in Algebra, Geometry, and Topology: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Topology in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Algebra, Geometry, and Topology: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Spectrum and Dynamics

Author : Dmitry Jakobson
Publisher : American Mathematical Soc.
ISBN 13 : 0821870467
Total Pages : 226 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Spectrum and Dynamics by : Dmitry Jakobson

Download or read book Spectrum and Dynamics written by Dmitry Jakobson and published by American Mathematical Soc.. This book was released on 2010-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers presented at the workshop on Spectrum and Dynamics held at the CRM in April 2008. In recent years. many new exciting connections have been established between the spectral theory of elliptic operators and the theory of dynamical systems. A number of articles in the proceedings highlight these discoveries. The volume features a diversity of topics. Such as quantum chaos, spectral geometry. Semiclassical analysis, number theory and ergodic theory. Apart from the research papers aimed at the experts, this book includes several survey articles accessible to a broad math ematical audience.

Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot

Author : Michel Laurent Lapidus
Publisher : American Mathematical Soc.
ISBN 13 : 9780821836378
Total Pages : 760 pages
Book Rating : 4.8/5 (363 download)

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Book Synopsis Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot by : Michel Laurent Lapidus

Download or read book Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot written by Michel Laurent Lapidus and published by American Mathematical Soc.. This book was released on 2004 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.

Positive Transfer Operators and Decay of Correlations

Author : Viviane Baladi
Publisher : World Scientific
ISBN 13 : 9789810233280
Total Pages : 332 pages
Book Rating : 4.2/5 (332 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 with total page 332 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.

Geometry and Analysis of Fractals

Author : De-Jun Feng
Publisher : Springer
ISBN 13 : 3662439204
Total Pages : 360 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Geometry and Analysis of Fractals by : De-Jun Feng

Download or read book Geometry and Analysis of Fractals written by De-Jun Feng and published by Springer. This book was released on 2014-08-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.