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

Published online by Cambridge University Press:  19 September 2008

Hans Henrik Rugh
Hans Henrik Rugh
Affiliation:
I.H.E.S., 35 route de Chartres, F-91440 Bures-sur-Yvette, France
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Abstract

We 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.

Type
Survey Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 4 , August 1996 , pp. 805 - 819
Copyright
Copyright © Cambridge University Press 1996

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