Dynamical zeta functions, Nielsen theory and Reidemeister torsion

Se p 19 96 Dynamical Zeta Functions , Nielsen Theory

Circle-Valued Morse Theory and Reidemeister Torsion

We compute an invariant counting gradient flow lines (including closed orbits) in S-valued Morse theory, and relate it to Reidemeister torsion for manifolds with χ = 0, b1 > 0. Here we extend the results in [6] following a different approach. However, this paper is written in a self-contained manner and may be read independently of [6]. The motivation of this work is twofold: on the one hand, i...

Reidemeister torsion in generalized Morse theory

In two previous papers with Yi-Jen Lee, we defined and computed a notion of Reidemeister torsion for the Morse theory of closed 1-forms on a finite dimensional manifold. The present paper gives an a priori proof that this Morse theory invariant is a topological invariant. It is hoped that this will provide a model for possible generalizations to Floer theory. In two papers with Yi-Jen Lee [HL1,...

Dynamical Zeta Functions

The study of periodic orbits for dynamical systems dates back to the very origins of the subject. Given a diieomorphism f : M ! M of a compact manifold it is a classical problem to count the number of periodic orbits fx; fx; : : : ; f n?1 xg, with f n x = x. For each n 1, we denote by N(n) the number of periodic points of period n. General Problem. What can we say about the numbers N(n)? What d...

Dynamical zeta functions

These notes are a rather subjective account of the theory of dynamical zeta functions. They correspond to three lectures presented by the author at the “Numeration” meeting in Leiden in 2010.