P- Omega Limit Set in Random Dynamical Systems

Abstract

The primary objective of this work is to investigate the idea of P-omega limit sets in a random dynamical system, where P might refer to any replete semi group in the time-space (considered a locally compact group with Harr measure). Within the context of a random dynamical system, the ideas of P-trajectory and P-invariant random sets are discussed; moreover, several fundamental features connected to these notions are looked into. The concept of a P-omega limit set of random sets in a random dynamical system is established, and several fundamental aspects are shown using mathematical proofs. In addition to this, the connection that exists between the P-trajectory and the P-omega limit set is shown.