Reidemeister and Nielsen zeta functions, and Reidemeister torsion in the theory of dynamical systems

1994 ◽  
pp. 123-145
Author(s):  
A. I. Felshtyn
Keyword(s):  
Dynamical Systems ◽  
Zeta Functions ◽  
Reidemeister Torsion

scholarly journals Dynamical zeta functions, congruences in Nielsen theory and Reidemeister torsion

1999 ◽  
Vol 49 (1) ◽  
pp. 77-116 ◽  
Author(s):  
Alexander Fel'shtyn ◽  
Richard Hill
Keyword(s):  
Zeta Functions ◽  
Reidemeister Torsion ◽  
Nielsen Theory

scholarly journals Generalized Fredholm determinants and Selberg zeta functions for Axiom A dynamical systems

1996 ◽  
Vol 16 (4) ◽  
pp. 805-819 ◽  
Author(s):  
Hans Henrik Rugh
Keyword(s):  
Dynamical Systems ◽  
Zeta Function ◽  
Complex Plane ◽  
Entire Functions ◽  
Fredholm Determinant ◽  
Three Dimensional ◽  
Zeta Functions ◽  
Selberg Zeta Function ◽  
Fredholm Determinants ◽  
Axiom A

AbstractWe consider a generalized Fredholm determinant d(z) and a generalized Selberg zeta function ζ(ω)−1 for Axiom A diffeomorphisms of a surface and Axiom A flows on three-dimensional manifolds, respectively. We show that d(z) and ζ(ω)−1 extend to entire functions in the complex plane. That the functions are entire and not only meromorphic is proved by a new method, identifying removable singularities by a change of Markov partitions.

scholarly journals Ruelle Zeta Functions of Hyperbolic Manifolds and Reidemeister Torsion

2021 ◽  
Author(s):  
Werner Müller
Keyword(s):  
Fundamental Group ◽  
General Result ◽  
Hyperbolic Manifold ◽  
Zeta Functions ◽  
Hyperbolic Manifolds ◽  
Reidemeister Torsion ◽  
Finite Dimensional ◽  
Orthogonal Representations ◽  
Ruelle Zeta Function ◽  
Complex Valued

AbstractThis paper is concerned with the behavior of twisted Ruelle zeta functions of compact hyperbolic manifolds at the origin. Fried proved that for an orthogonal acyclic representation of the fundamental group of a compact hyperbolic manifold, the twisted Ruelle zeta function is holomorphic at $$s=0$$ s = 0 and its value at $$s=0$$ s = 0 equals the Reidemeister torsion. He also established a more general result for orthogonal representations, which are not acyclic. The purpose of the present paper is to extend Fried’s result to arbitrary finite dimensional representations of the fundamental group. The Reidemeister torsion is replaced by the complex-valued combinatorial torsion introduced by Cappell and Miller.

scholarly journals Zeta functions and dynamical systems

Nonlinearity ◽  
2006 ◽  
Vol 19 (10) ◽  
pp. 2467-2473 ◽  
Author(s):  
Carlangelo Liverani ◽  
Masato Tsujii
Keyword(s):  
Dynamical Systems ◽  
Zeta Functions
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