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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Markov extensions, zeta functions, and Fredholm theory for piecewise invertible dynamical systems


Author: G. Keller
Journal: Trans. Amer. Math. Soc. 314 (1989), 433-497
MSC: Primary 58F11; Secondary 28D99, 47B99, 54H20, 58F20
MathSciNet review: 1005524
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Abstract: Transfer operators and zeta functions of piecewise monotonic and of more general piecewise invertible dynamical systems are studied. To this end we construct Markov extensions of given systems, develop a kind of Fredholm theory for them, and carry the results back to the original systems. This yields e.g. bounds on the number of ergodic maximal measures or equilibrium states.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-1005524-4
PII: S 0002-9947(1989)1005524-4
Article copyright: © Copyright 1989 American Mathematical Society