Electronic ISBN:  9781470402907 
Product Code:  MEMO/147/699.E 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 147; 2000; 146 ppMSC: Primary 58; Secondary 55; 57;
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.
ReadershipGraduate students and research mathematicians interested in global analysis, analysis on manifolds.

Table of Contents

Chapters

Introduction

1. Nielsen fixed point theory

2. The Reidemeister zeta function

3. The Nielsen zeta function

4. Reidemeister and Nielsen zeta functions modulo normal subgroup, minimal dynamical zeta functions

5. Congruences for Reidemeister and Nielsen numbers

6. The Reidemeister torsion


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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.
Graduate students and research mathematicians interested in global analysis, analysis on manifolds.

Chapters

Introduction

1. Nielsen fixed point theory

2. The Reidemeister zeta function

3. The Nielsen zeta function

4. Reidemeister and Nielsen zeta functions modulo normal subgroup, minimal dynamical zeta functions

5. Congruences for Reidemeister and Nielsen numbers

6. The Reidemeister torsion