ON THE ERGODIC SHADOWING PROPERTY THROUGH UNIFORM LIMITS

ON THE ERGODIC SHADOWING PROPERTY THROUGH UNIFORM LIMITS

In this paper, we study some dynamics of the uniform limits of sequences in dynamical systems on a noncompact metric space. We show that if a sequence of homeomorphisms on a noncompact metric space has the uniform ergodic shadowing property, then the uniform limit also has the ergodic shadowing property. Then we apply this result to nonwandering maps.

1. Introduction and preliminaries

2. Proof of Theorem 1.1

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