Subadditive Pre-Image Variational Principle for Bundle Random Dynamical Systems

Abstract

A central role in the variational principle of the measure preserving transformations is played by the topological pressure. We introduce subadditive pre-image topological pressure and pre-image measure-theoretic entropy properly for the random bundle transformations on a class of measurable subsets. On the basis of these notions, we are able to complete the subadditive pre-image variational principle under relatively weak conditions for the bundle random dynamical systems.

The Topological Entropy Conjecture

“…Lately, for results about random entropy expansiveness and dominated splittings, see [38], and for results about the relations of topological entropy and Lefschetz numbers, see [39][40][41]. Furthermore, for a variational principle for subadditive preimage topological pressure for continuous bundle random dynamical systems, see [42].…”