Generic Homeomorphisms have the Pseudo-Orbit Tracing Property

Odani, Kenzi

doi:10.2307/2048270

Cited by 4 publications

(2 citation statements)

References 7 publications

(7 reference statements)

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“…The study of the invariant measures for typical maps was initiated recently by Abdenur and Andersson [AA]. Previously studies of the dynamics of typical maps have concentrated on the topological properties; see [AHK,AP,H1,H2,KMOP,O,OU,PP,Y] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Invariant measures for typical continuous maps on manifolds

Catsigeras

Troubetzkoy

2019

Nonlinearity

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We study the invariant measures of typical C 0 maps on compact connected manifolds with or without boundary, and also of typical homeomorphisms. We prove that the weak * closure of the set of ergodic measures coincides with the weak * closure of the set of measures supported on periodic orbits and also coincides with the set of pseudo-physical measures. Furthermore, we show that this set has empty interior in the set of invariant measures.

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Section: Introductionmentioning

confidence: 99%

Invariant measures for typical continuous maps on manifolds

Catsigeras

Troubetzkoy

2019

Nonlinearity

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“…In particular, many genericity results exist for manifolds. Yano [37] demonstrated that shadowing is generic among homeomorphisms of the unit circle, Odani [26] extended this result to smooth manifolds of dimension at most three, and Pilyugin and Plamenevskaya [31] further extended this result to compact manifolds without boundary which have a handle decomposition. Results concerning the more general class of continuous maps include those of Mizera [24], who demonstrated that shadowing is generic in C(X) where X is an arc or circle, and those of Kościelniak, Mazur, Oprocha and Pilarczyk [18], who extended this result to C(X) and S(X) where X is a compact manifold.…”

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confidence: 99%

On genericity of shadowing in one dimension

Meddaugh

2021

Fund. Math.

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On the genericity of the shadowing property for conservative homeomorphisms

Guihéneuf

Lefeuvre

2018

Proc. Amer. Math. Soc.

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Abstract. We prove the genericity of the shadowing and periodic shadowing properties for both conservative and dissipative homeomorphisms on a compact connected manifold. Our proof is valid for topological manifolds and still holds in the dissipative case. As a consequence of this result, we establish the genericity of the specification property, the average shadowing property and the asymptotic average shadowing property in the conservative case.

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Generic Homeomorphisms have the Pseudo-Orbit Tracing Property

Abstract: Abstract.Let M (dimA/<3) be a compact manifold. Then a generic fe Homeo(A/) satisfies the following: / has the pseudo-orbit tracing property; / is C tolerance stable; and / is not topologically stable.

Cited by 4 publications

References 7 publications

Invariant measures for typical continuous maps on manifolds

Invariant measures for typical continuous maps on manifolds

On genericity of shadowing in one dimension

On the genericity of the shadowing property for conservative homeomorphisms

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