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Theoretical exploration investigates induced entropy concepts in random dynamical systems, highlighting implications for ergodic systems.
In this paper, we introduce the concepts of induced topological entropy and induced measure-theoretic entropy for random dynamical systems. By providing the topological version of induced measure-theoretic entropy, we establish the Katok entropy formula for a continuous bundle random dynamical system over an invertible ergodic system. We also consider the induced version with lower and upper pointwise dimensions, and establish a measure-theoretic entropy formula for lower and upper induced pointwise dimensions for a continuous bundle random dynamical system over an invertible ergodic system.
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Yang et al. (2022) studied this question.
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