Dynamical zeta functions for maps of the interval

Author:
David Ruelle

Journal:
Bull. Amer. Math. Soc. **30** (1994), 212-214

MSC (2000):
Primary 58F20; Secondary 58F03

DOI:
https://doi.org/10.1090/S0273-0979-1994-00489-6

MathSciNet review:
1246470

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Abstract | References | Similar Articles | Additional Information

Abstract: A dynamical zeta function and a transfer operator are associated with a piecewise monotone map of the interval [0, 1] and a weight function . The analytic properties of and the spectral properties of are related by a theorem of Baladi and Keller under an assumption of "generating partition". It is shown here how to remove this assumption and, in particular, extend the theorem of Baladi and Keller to the case when has negative Schwarzian derivative.

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Additional Information

DOI:
https://doi.org/10.1090/S0273-0979-1994-00489-6

Keywords:
Zeta function,
transfer operator,
topological pressure,
interval map

Article copyright:
© Copyright 1994
American Mathematical Society