| Abstract: |
| In this talk, we introduce various shadowing properties such as Hausdorff average shadowing property, Hausdorff ergodic shadowing property, periodic shadowing property when the phase space is a general topological space. We prove some related results. On a compact Hausdorff space, if $f$ has the Hausdorff average shadowing property, we show that $f^k$ has the Hausdorff average shadowing property for every positive integer $k$. Further, we show that a dynamical system with the Hausdorff ergodic shadowing property is Hausdorff chain transitive if $f$ is surjective. The content of the talk is from the following references.
[1]POSITIVE EXPANSIVITY, CHAIN TRANSITIVITY,
RIGIDITY, AND SPECIFICATION ON GENERAL
TOPOLOGICAL SPACES, Bull. Korean Math. Soc. 59 (2022), No. 2.
[2] ON PERIODIC SHADOWING, TRANSITIVITY, CHAIN
MIXING AND EXPANSIVITY IN UNIFORM DYNAMICAL
SYSTEMS, Gulf Journal of Mathematics
Vol 9, Issue 2 (2020).
[3] ERGODIC SHADOWING, d-SHADOWING AND
EVENTUAL SHADOWING IN TOPOLOGICAL SPACES, Nonlinear Functional Analysis and Applications
Vol. 27, No. 4 (2022). |
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