ScholarWorks@성균관대학교

초록

We provide a stochastic characterization of the classical shadowing property of dynamical systems. Then, we reformulate stochastic stability for differentiable systems as well as topological dynamical systems. We also investigate the stability of the set of invariant measures for homeomorphisms on compact metric spaces under C0$C{<}^{>}0$-perturbations. We explore alternative distances, such as the random distance, and introduce the concept of random-stable homeomorphism. These results reveal that while every topologically stable homeomorphism of a compact metric space is also random-stable, the converse is not always true. We analyze the recurrent set and the chain recurrent set of a random-stable homeomorphism on compact manifolds.

키워드