Topologically stable points and uniform limits
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In this paper we study a pointwise version of Walters topological stability in the class of homeomorphisms on a compact metric space. We also show that if a sequence of homeomorphisms on a compact metric space is uniformly expansive with the uniform shadowing property, then the limit is expansive with the shadowing property and so topologically stable. Furthermore, we give examples to illustrate our results.
Abstract
In this paper we study a pointwise version of Walters topological stability in the class of homeomorphisms on a compact metric space. We also show that if a sequence of homeomorphisms on a compact metric space is uniformly expansive with the uniform shadowing property, then the limit is expansive with the shadowing property and so topologically stable. Furthermore, we give examples to illustrate our results.
참고문헌 (15)
- N. Aoki, "Topological theory of dynamical systems", pp.52~ (1994), North-Holland Mathematical Library
- J. Aponte, "Shadowable points for flows", J. Dyn. Control Syst, 24(4), pp.701~719 (2018)[DOI]
- A. Arbieto, "Positive entropy through pointwise dynamics", Proc. Amer. Math. Soc, 148(1), pp.263~271 (2020)[DOI]
- L. Fernandez, "Shadowing for induced maps of hyperspaces", Fund. Math, 235(3), pp.277~286 (2016)[DOI]
- N. Kawaguchi, "Quantitative shadowable points", Dyn. Syst, 32(4), pp.504~518 (2017)[DOI]
- A. G. Khan, "Stability theorems in pointwise dynamics", Topology Appl, 320, pp.14~ (2022)[DOI]
- N. Koo, "Pointwise topological stability", 61(4), pp.1179~1191 (2018)[DOI]
- 구남집, "ON THE ALMOST SHADOWING PROPERTY FOR HOMEOMORPHISMS", 충청수학회지, 35(4), pp.329~333 (2022), 충청수학회
- K. Lee, "On almost shadowable measures", Russ. J. Nonlinear Dyn, 18(2), pp.297~307 (2022)[DOI]
- K. Lee, "Points which satisfy the closing lemma", Far East J. Math. Sci, 3(2), pp.171~177 (1995)
- C. A. Morales Rojas, "Shadowable points", Dyn. Syst, 31(3), pp.347~356 (2016)[DOI]
- A. Morimoto, "Manifolds and Lie groups (Notre Dame, Ind., 1980)", pp.283~299 (1981), Birkhauser
- S. Y. Pilyugin, "Lecture Notes in Mathematics", pp.1706~ (1999), Springer
- W. R. Utz, "Unstable homeomorphisms", Proc. Amer. Math. Soc, 1, pp.769~774 (1950)[DOI]
- P. Walters, "On the pseudo-orbit tracing property and its relationship to stability", Proc. Conf., North Dakota State Univ, pp.231~244 (1978), Springer