Expanding measure has nonuniform specification property on random dynamical system

Abstract

In the present paper, we study the distribution of the return points in the fibers for a RDS (random dynamical systems) nonuniformly expanding preserving an ergodic probability, we also show the abundance of nonlacunarity of hyperbolic times that are obtained along the orbits through the fibers. We conclude that any ergodic measure with positive Lyapunov exponents satisfies the nonuniform specification property between fibers. As consequences, we prove that any expanding measure is the limit of probability measure whose measures of disintegration on the fibers are supported by a finite number of return points and we prove that the average of the measures on the fibers corresponding to a disintegration, along an orbit in the base dynamics is the limit of Dirac measures supported in return orbits on the fibers.

References in corpus (5)

• Equilibrium States for Random Non-uniformly Expanding Maps
• Thermodynamic formalism for random non-uniformly expanding maps
• Absolutely continuous invariant measures for random non-uniformly expanding maps
• Distance Expanding Random Mappings, Thermodynamic Formalism, Gibbs Measures, and Fractal Geometry
• Uniqueness and Stability of Equilibrium States for Random Non-uniformly Expanding Maps