Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.