A complex Ruelle-Perron-Frobenius theorem and two counterexamples

  title={A complex Ruelle-Perron-Frobenius theorem and two counterexamples},
  author={Mark Pollicott},
  journal={Ergodic Theory and Dynamical Systems},
  pages={135 - 146}
  • M. Pollicott
  • Published 1 March 1984
  • Mathematics
  • Ergodic Theory and Dynamical Systems
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. 
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