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On the fixed points of the Ruelle operator

Part of: Ergodic theory Complex dynamical systems

Published online by Cambridge University Press:  10 January 2020

CARLOS CABRERA Open the ORCID record for CARLOS CABRERA [Opens in a new window]  and
PETER MAKIENKO Open the ORCID record for PETER MAKIENKO [Opens in a new window]
CARLOS CABRERA
Affiliation:
Universidad Nacional Autónoma de Mexico, Unidad Cuernavaca del Instituto de Matemáticas, Av. Universidad S/N. C.U., Cuernavaca, Morelos 62210, Mexico email carloscabrerao@im.unam.mx, makienko@im.unam.mx
PETER MAKIENKO
Affiliation:
Universidad Nacional Autónoma de Mexico, Unidad Cuernavaca del Instituto de Matemáticas, Av. Universidad S/N. C.U., Cuernavaca, Morelos 62210, Mexico email carloscabrerao@im.unam.mx, makienko@im.unam.mx
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Abstract

We discuss the relation between the existence of fixed points of the Ruelle operator acting on different Banach spaces, and Sullivan’s conjecture in holomorphic dynamics.

Keywords

low dimensional dynamicsclassical ergodic theoryquasiconfrmal methods and Teichmuller theory

MSC classification

Primary: 37F10: Polynomials; rational maps; entire and meromorphic functions 37A30: Ergodic theorems, spectral theory, Markov operators 37F30: Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 4 , April 2021 , pp. 1025 - 1063
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Copyright
© Cambridge University Press, 2020

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