Random ergodic theorems for sub-Markovian operators
Random homogenization of an obstacle problem
Random Markov Mappings.
Randomly connected dynamical systems - asymptotic stability
We give sufficient conditions for asymptotic stability of a Markov operator governing the evolution of measures due to the action of randomly chosen dynamical systems. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure for the semigroup generated by the system.
Rank and spectral multiplicity
For a dynamical system (X,T,μ), we investigate the connections between a metric invariant, the rank r(T), and a spectral invariant, the maximal multiplicity m(T). We build examples of systems for which the pair (m(T),r(T)) takes values (m,m) for any integer m ≥ 1 or (p-1, p) for any prime number p ≥ 3.
Ratio Tauberian theorems for relatively bounded functions and sequences in Banach spaces
We prove ratio Tauberian theorems for relatively bounded functions and sequences in Banach spaces.
Rectangle Exchange Transformations.
Reduction of a mean ergodic Markov semigroup on C(X) into its irreducible components.
Reformulation et extension de certains théorèmes ergodiques
Répartition et ergodicité
Rigidity of Furstenberg entropy for semisimple Lie group actions
Rotation methods in operator ergodic theory.