scholarly journals The Ruelle operator for symmetric $\beta$-shifts

2020 ◽  
Vol 64 ◽  
pp. 661-680
Author(s):  
Artur O. Lopes ◽  
Victor Vargas
Keyword(s):  
Ruelle Operator

scholarly journals Ruelle operator theorem for non-expansive systems

2009 ◽  
Vol 30 (2) ◽  
pp. 469-487 ◽  
Author(s):  
YUNPING JIANG ◽  
YUAN-LING YE
Keyword(s):  
Dynamical Systems ◽  
Sufficient Conditions ◽  
Iterated Function Systems ◽  
Ruelle Operator ◽  
Iterated Function

AbstractThe Ruelle operator theorem has been studied extensively both in dynamical systems and iterated function systems. In this paper we study the Ruelle operator theorem for non-expansive systems. Our theorems give some sufficient conditions for the Ruelle operator theorem to be held for a non-expansive system.

A PROOF OF THE RUELLE OPERATOR THEOREM

1995 ◽  
Vol 07 (08) ◽  
pp. 1241-1247 ◽  
Author(s):  
AI HUA FAN
Keyword(s):  
Ruelle Operator

We give a new proof of the Ruelle operator theorem by using a setup inspired by the G-measure formalism due to Brown-Dooley.

scholarly journals Dissipative conformal measures on locally compact spaces

2014 ◽  
Vol 36 (2) ◽  
pp. 649-670 ◽  
Author(s):  
KLAUS THOMSEN
Keyword(s):  
Operator Algebras ◽  
Sufficient Conditions ◽  
Locally Compact ◽  
Compact Spaces ◽  
Ruelle Operator ◽  
Conformal Measures ◽  
Continuous Potential ◽  
The One ◽  
Necessary And Sufficient ◽  
Uniformly Continuous

The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among other things, the method is used to give necessary and sufficient conditions for the existence of eigenmeasures for the dual Ruelle operator associated to a locally compact non-compact irreducible Markov shift equipped with a uniformly continuous potential function. As an application to operator algebras the results are used to determine for which ${\it\beta}$ there are gauge invariant ${\it\beta}$-KMS weights on a simple graph $C^{\ast }$-algebra when the one-parameter automorphism group is given by a uniformly continuous real-valued function on the path space of the graph.

scholarly journals Spectral properties of the Ruelle operator on the Walters class over compact spaces

Nonlinearity ◽  
2016 ◽  
Vol 29 (8) ◽  
pp. 2253-2278 ◽  
Author(s):  
Leandro Cioletti ◽  
Eduardo A Silva
Keyword(s):  
Spectral Properties ◽  
Compact Spaces ◽  
Ruelle Operator

scholarly journals Eigenfunctions of the Laplacian and associated Ruelle operator

Nonlinearity ◽  
2008 ◽  
Vol 21 (10) ◽  
pp. 2239-2253 ◽  
Author(s):  
A O Lopes ◽  
Ph Thieullen
Keyword(s):  
Ruelle Operator
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