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A complex Ruelle-Perron-Frobenius theorem and two counterexamples

Published online by Cambridge University Press:  19 September 2008

Mark Pollicott
Mark Pollicott
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, England
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Abstract

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In this paper a new proof of a theorem of Ruelle about real Perron-Frobenius type operators is given. This theorem is then extended to complex Perron-Frobenius type operators in analogy with Wielandt's theorem for matrices. Finally two questions raised by Ruelle and Bowen concerning analyticity properties of zeta functions for flows are answered.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 1 , March 1984 , pp. 135 - 146
Copyright
Copyright © Cambridge University Press 1984

References

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