6533b873fe1ef96bd12d4b64

RESEARCH PRODUCT

On the existence of conditionally invariant probability measures in dynamical systems

Véronique Maume-deschampsVéronique Maume-deschampsServet MartínezPierre Collet

subject

Discrete mathematicsClass (set theory)Dynamical systems theoryApplied MathematicsGeneral Physics and AstronomyStatistical and Nonlinear PhysicsAbsolute continuityRandom measurePolish spaceInvariant measureInvariant (mathematics)Mathematical PhysicsProbability measureMathematics

description

Let T : X→X be a measurable map defined on a Polish space X and let Y be a non-trivial subset of X. We give conditions ensuring the existence of conditionally invariant probability measures to non-absorption in Y. For dynamics which are non-singular with respect to some fixed probability measure we supply sufficient conditions for the existence of absolutely continuous conditionally invariant measures. These conditions are satisfied for a wide class of dynamical systems including systems that are Φ-mixing and Gibbs.

yearjournalcountryeditionlanguage
2000-06-01Nonlinearity
https://doi.org/10.1088/0951-7715/13/4/315