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doi:10.1016/S0375-9601(97)00976-6 
Copyright © 1998 Published by Elsevier Science B.V.
Spectral decomposition of expanding probabilistic dynamical systems
a International Solvay Institutes for Physics and Chemistry, C.P. 231, Campus Plaine ULB, Bd. du Triomphe, 1050, Brussels, Belgium b Theoretische Natuurkunde, Free University of Brussels, Brussels, Belgium c Departamento de Fisica, Universidade Federal do Espirito Santo, 29060-900, Vitoria, ES, Brazil d Hugo Steinhaus Center and Institute of Mathematics, Wroclaw Technical University, ul. Wybrze
e Wyspia
skiego 27, 50-370, Wroclaw, Poland
Received 8 May 1997;
Revised 16 December 1997;
accepted 16 December 1997
Communicated by C.R. Doering
Available online 19 June 1998.
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Abstract
We study probabilistic combinations of expanding dynamical systems, which we call expanding probabilistic dynamical systems, in one dimension. If the system is composed by exact endomorphisms we prove that the probabilistic dynamical system is an exact Markov semigroup, and we determine a generalized spectral decomposition of the associated Markov operator on densities for an example of the tent map coupled with the 2-Renyi map.
