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Dynamical Zeta Functions Nielsen Theory And Reidemeister Torsion
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Book Synopsis Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion by : Alexander Fel'shtyn
Download or read book Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion written by Alexander Fel'shtyn and published by American Mathematical Soc.. This book was released on 2000 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the paper we study new dynamical zeta functions connected with Nielsen fixed point theory. The study of dynamical zeta functions is part of the theory of dynamical systems, but it is also intimately related to algebraic geometry, number theory, topology and statistical mechanics. The paper consists of four parts. Part I presents a brief account of the Nielsen fixed point theory. Part II deals with dynamical zeta functions connected with Nielsen fixed point theory. Part III is concerned with analog of Dold congruences for the Reidemeister and Nielsen numbers. In Part IV we explain how dynamical zeta functions give rise to the Reidemeister torsion, a very important topological invariant which has useful applications in knots theory,quantum field theory and dynamical systems.
Book Synopsis Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion by : Alexander L. Fel'shtyn
Download or read book Dynamical Zeta Functions, Nielsen Theory and Reidemeister Torsion written by Alexander L. Fel'shtyn and published by . This book was released on 1992 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dynamical zeta functions, Nielsen theory and Reidemeister torsion by : Aleksandr L. Fel'štyn
Download or read book Dynamical zeta functions, Nielsen theory and Reidemeister torsion written by Aleksandr L. Fel'štyn and published by . This book was released on 1998 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Reidemeister, Nielsen zeta functions and the Reidemeister torsion in dynamical systems theory by : Aleksandr L. Fel'štyn
Download or read book The Reidemeister, Nielsen zeta functions and the Reidemeister torsion in dynamical systems theory written by Aleksandr L. Fel'štyn and published by . This book was released on 1991 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nielsen Theory and Dynamical Systems by : Christopher Keil McCord
Download or read book Nielsen Theory and Dynamical Systems written by Christopher Keil McCord and published by American Mathematical Soc.. This book was released on 1993 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Nielsen Theory and Dynamical Systems, held in June 1992 at Mount Holyoke College. Focusing on the interface between Nielsen fixed point theory and dynamical systems, this book provides an almost complete survey of the state of the art of Nielsen theory. Most of the articles are expository, making them accessible to both graduate students and researchers in algebraic topology, fixed point theory, and dynamical systems.
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.
Book Synopsis Dynamics: Topology and Numbers by : Pieter Moree
Download or read book Dynamics: Topology and Numbers written by Pieter Moree and published by American Mathematical Soc.. This book was released on 2020-02-12 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2–6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics. The volume is dedicated to the memory of Sergiy Kolyada and also contains some personal accounts of his life and mathematics.
Book Synopsis Noncommutative Geometry and Number Theory by : Caterina Consani
Download or read book Noncommutative Geometry and Number Theory written by Caterina Consani and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.
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 315 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.
Book Synopsis Handbook of Topological Fixed Point Theory by : Robert F. Brown
Download or read book Handbook of Topological Fixed Point Theory written by Robert F. Brown and published by Springer Science & Business Media. This book was released on 2005-07-21 with total page 990 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will be especially useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.
Book Synopsis Circle-valued Morse Theory by : Andrei V. Pajitnov
Download or read book Circle-valued Morse Theory written by Andrei V. Pajitnov and published by Walter de Gruyter. This book was released on 2006-01-01 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1927 M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. This became a starting point of the Morse theory which is now one of the basic parts of differential topology. It is a large and actively developing domain of differential topology, with applications and connections to many geometrical problems. The aim of the present book is to give a systematic treatment of the geometric foundations of a subfield of that topic, the circle-valued Morse functions, a subfield of Morse theory.
Book Synopsis Geometry and Topology of Submanifolds and Currents by : Weiping Li
Download or read book Geometry and Topology of Submanifolds and Currents written by Weiping Li and published by American Mathematical Soc.. This book was released on 2015-08-25 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: he papers in this volume are mainly from the 2013 Midwest Geometry Conference, held October 19, 2013, at Oklahoma State University, Stillwater, OK, and partly from the 2012 Midwest Geometry Conference, held May 12-13, 2012, at the University of Oklahoma, Norman, OK. The papers cover recent results on geometry and topology of submanifolds. On the topology side, topics include Plateau problems, Voevodsky's motivic cohomology, Reidemeister zeta function and systolic inequality, and freedom in 2- and 3-dimensional manifolds. On the geometry side, the authors discuss classifying isoparametric hypersurfaces and review Hartogs triangle, finite volume flows, nonexistence of stable p-currents, and a generalized Bernstein type problem. The authors also show that the interaction between topology and geometry is a key to deeply understanding topological invariants and the geometric problems.
Book Synopsis Fixed Point Theory by : Andrzej Granas
Download or read book Fixed Point Theory written by Andrzej Granas and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Fixed Points is one of the most powerful tools of modern mathematics. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications. From the reviews: "I recommend this excellent volume on fixed point theory to anyone interested in this core subject of nonlinear analysis." --MATHEMATICAL REVIEWS
Book Synopsis L2-Invariants: Theory and Applications to Geometry and K-Theory by : Wolfgang Lück
Download or read book L2-Invariants: Theory and Applications to Geometry and K-Theory written by Wolfgang Lück and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.
Book Synopsis On the Foundations of Nonlinear Generalized Functions I and II by : Michael Grosser
Download or read book On the Foundations of Nonlinear Generalized Functions I and II written by Michael Grosser and published by American Mathematical Soc.. This book was released on 2001 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: In part 1 we construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and applications to nonlinear differential equations involving singularities are given. Part 2 gives a comprehensive analysis of algebras of Colombeau-type generalized functions in the range between the diffeomorphism-invariant quotient algebra ${\mathcal G}^d = {\mathcal E}_M/{\mathcal N}$ introduced in part 1 and Colombeau's original algebra ${\mathcal G}^e$.Three main results are established: first, a simple criterion describing membership in ${\mathcal N}$ (applicable to all types of Colombeau algebras) is given; second, two counterexamples demonstrate that ${\mathcal G}^d$ is not injectively included in ${\mathcal G}^e$; and finally, it is shown that in the range ""between"" ${\mathcal G}^d$ and ${\mathcal G}^e$ only one more construction leads to a diffeomorphism invariant algebra. In analyzing the latter, several classification results essential for obtaining an intrinsic description of ${\mathcal G}^d$ on manifolds are derived.
Book Synopsis Smooth Molecular Decompositions of Functions and Singular Integral Operators by : John E. Gilbert
Download or read book Smooth Molecular Decompositions of Functions and Singular Integral Operators written by John E. Gilbert and published by American Mathematical Soc.. This book was released on 2002 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Under minimal assumptions on a function $\psi$ the authors obtain wavelet-type frames of the form $\psi_{j, k}(x) = r DEGREES{(1/2)n j} \psi(r DEGREESj x - sk), j \in \integer, k \in \integer DEGREESn, $ for some $r > 1$ and $s > 0$. This collection is shown to be a frame for a scale of Triebel-Lizorkin spaces (which includes Lebesgue, Sobolev and Hardy spaces) and the reproducing formula converges in norm as well as pointwise a.e. The construction follows from a characterization of those operators which are bounded on a space of smooth molecules. This characterization also allows us to decompose a broad range of singular integral operators in ter
Book Synopsis Generalized Whittaker Functions on $SU(2,2)$ with Respect to the Siegel Parabolic Subgroup by : Yasuro Gon
Download or read book Generalized Whittaker Functions on $SU(2,2)$ with Respect to the Siegel Parabolic Subgroup written by Yasuro Gon and published by American Mathematical Soc.. This book was released on 2002 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Obtains an explicit formula for generalized Whittaker functions and multiplicity one theorem for all discrete series representations of $SU(2,2)$.
