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