Cohomological Theory Of Dynamical Zeta Functions

Author : Andreas Juhl
Publisher : Birkhäuser
ISBN 13 : 3034883404
Total Pages : 712 pages
Book Rating : 4.05/5 ( download)

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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.

Author : Alexander Fel'shtyn
Publisher : American Mathematical Soc.
ISBN 13 : 0821820907
Total Pages : 165 pages
Book Rating : 4.02/5 ( download)

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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.

Author : David Ruelle
Publisher : American Mathematical Soc.
ISBN 13 : 9780821836019
Total Pages : 74 pages
Book Rating : 4.13/5 ( download)

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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 74 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.

Author : Yuri Tschinkel
Publisher : Universitätsverlag Göttingen
ISBN 13 : 3938616776
Total Pages : 168 pages
Book Rating : 4.72/5 ( download)

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Download or read book Algebraic Groups written by Yuri Tschinkel and published by Universitätsverlag Göttingen. This book was released on 2007 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Alexander L. Fel'shtyn
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.00/5 ( download)

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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:

Author : Erich Kähler
Publisher : Walter de Gruyter
ISBN 13 : 9783110171181
Total Pages : 986 pages
Book Rating : 4.8X/5 ( download)

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Download or read book Mathematical Works written by Erich Kähler and published by Walter de Gruyter. This book was released on 2003 with total page 986 pages. Available in PDF, EPUB and Kindle. Book excerpt: For most mathematicians and many mathematical physicists the name Erich Kähler is strongly tied to important geometric notions such as Kähler metrics, Kähler manifolds and Kähler groups. They all go back to a paper of 14 pages written in 1932. This, however, is just a small part of Kähler's many outstanding achievements which cover an unusually wide area: From celestial mechanics he got into complex function theory, differential equations, analytic and complex geometry with differential forms, and then into his main topic, i.e. arithmetic geometry where he constructed a system of notions which is a precursor and, in large parts, equivalent to the now used system of Grothendieck and Dieudonné. His principal interest was in finding the unity in the variety of mathematical themes and establishing thus mathematics as a universal language. In this volume Kähler's mathematical papers are collected following a "Tribute to Herrn Erich Kähler" by S. S. Chern, an overview of Kähler's life data by A. Bohm and R. Berndt, and a Survey of his Mathematical Work by the editors. There are also comments and reports on the developments of the main topics of Kähler's work, starting by W. Neumann's paper on the topology of hypersurface singularities, J.-P. Bourguignon's report on Kähler geometry and, among others by Berndt, Bost, Deitmar, Ekeland, Kunz and Krieg, up to A. Nicolai's essay "Supersymmetry, Kähler geometry and Beyond". As Kähler's interest went beyond the realm of mathematics and mathematical physics, any picture of his work would be incomplete without touching his work reaching into other regions. So a short appendix reproduces three of his articles concerning his vision of mathematics as a universal Theme together with an essay by K. Maurin giving an "Approach to the philosophy of Erich Kähler".

Author : Jean-Philippe Anker
Publisher : Springer Science & Business Media
ISBN 13 : 0817681922
Total Pages : 331 pages
Book Rating : 4.20/5 ( download)

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Download or read book Lie Theory written by Jean-Philippe Anker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: * First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.

Author : Gerard van der Geer
Publisher : Springer Science & Business Media
ISBN 13 : 9780817643973
Total Pages : 342 pages
Book Rating : 4.74/5 ( download)

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Download or read book Number Fields and Function Fields – Two Parallel Worlds written by Gerard van der Geer and published by Springer Science & Business Media. This book was released on 2005-09-14 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Invited articles by leading researchers explore various aspects of the parallel worlds of function fields and number fields Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives Aimed at graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections

Author : Venkatrama Lakshmibai
Publisher : Springer Science & Business Media
ISBN 13 : 9783764304447
Total Pages : 598 pages
Book Rating : 4.48/5 ( download)

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Download or read book A Tribute to C.S. Seshadri written by Venkatrama Lakshmibai and published by Springer Science & Business Media. This book was released on 2003-07-24 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: C.S. Seshadri turned seventy on the 29th of February, 2002. To mark this occasion, a symposium was held in Chennai, India, where some of his colleagues gave expository talks highlighting Seshadri's contributions to mathematics. This volume includes expanded texts of these talks as well as research and expository papers on geometry and representation theory. It will serve as an excellent reference for researchers and students in these areas.

Author : Gregory Arone
Publisher : Springer Science & Business Media
ISBN 13 : 9783764304003
Total Pages : 322 pages
Book Rating : 4.06/5 ( download)

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Download or read book Categorical Decomposition Techniques in Algebraic Topology written by Gregory Arone and published by Springer Science & Business Media. This book was released on 2003-11-27 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of articles at the frontier of current research in Algebraic Topology. It presents recent results by top notch experts, and is intended primarily for researchers and graduate students working in the field of algebraic topology. Included is an important article by Cohen, Johnes and Yan on the homology of the space of smooth loops on a manifold M, endowed with the Chas-Sullivan intersection product, as well as an article by Goerss, Henn and Mahowald on stable homotopy groups of spheres, which uses the cutting edge technology of "topological modular forms".