A complex Ruelle-Perron-Frobenius theorem and two counterexamples
- 1 March 1984
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 4 (1) , 135-146
- https://doi.org/10.1017/s0143385700002327
Abstract
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.Keywords
This publication has 2 references indexed in Scilit:
- Examples for the Nonuniqueness of the Equilibrium StateTransactions of the American Mathematical Society, 1977
- Ruelle's Operator Theorem and g-MeasuresTransactions of the American Mathematical Society, 1975