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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

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
MathSciNet review: 1246470
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Abstract: A dynamical zeta function $ \zeta $ and a transfer operator $ \mathcal{L}$ are associated with a piecewise monotone map $ f$ of the interval [0, 1] and a weight function $ g$. The analytic properties of $ \zeta $ and the spectral properties of $ \mathcal{L}$ 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 $ f$ has negative Schwarzian derivative.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1994-00489-6
PII: S 0273-0979(1994)00489-6
Keywords: Zeta function, transfer operator, topological pressure, interval map
Article copyright: © Copyright 1994 American Mathematical Society