Hyperbolicity and types of shadowing for $C^1$ generic vector fields

Ribeiro, Raquel

doi:10.3934/dcds.2014.34.2963

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Introduction2

Theorem a Anosov Families Admit Canonical Coordinates1

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Cited by 13 publications

(11 citation statements)

References 31 publications

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“…We would like to thank Raquel Ribeiro for pointing us out that she also proved independently, in[32], this same result.…”

supporting

confidence: 58%

Shadowing, expansiveness and specification for C1-conservative systems

Bessa

Lee

Xiao

2015

Acta Mathematica Scientia

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Abstract. We prove that a C 1 -generic volume-preserving dynamical system (diffeomorphism or flow) has the shadowing property or is expansive or has the weak specification property if and only if it is Anosov. Finally, as in [9,21], we prove that the C 1 -robustness, within the volume-preserving context, of the expansiveness property and the weak specification property, imply that the dynamical system (diffeomorphism or flow) is Anosov.

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“…We would like to thank Raquel Ribeiro for pointing us out that she also proved independently, in[32], this same result.…”

supporting

confidence: 58%

Shadowing, expansiveness and specification for C1-conservative systems

Bessa

Lee

Xiao

2015

Acta Mathematica Scientia

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“…Many authors has studied this properties and your relation with the hiperbolicity, for example, [19], [20], [22] and [25]. And also, in many contexts, as in [4], [5] and [21]. Thus, to decide which systems possess the shadowing property is an important problem in dynamics.…”

Section: Theorem a Anosov Families Admit Canonical Coordinatesmentioning

confidence: 99%

Expansiveness, Shadowing and Markov Partition for Anosov Families

Jeovanny¹,

Ribeiro²

2020

Preprint

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“…[47, Lemma 23] If X has the limit shadowing property then W s (O) ∩ W u (O ′ ) = ∅ for any pair of orbits O, O ′ ∈ Crit(X).…”

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confidence: 99%

Conservative flows with various types of shadowing

Bessa

Ribeiro

2015

Chaos, Solitons & Fractals

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In the present paper we study the C 1 -robustness of the three properties: average shadowing, asymptotic average shadowing and limit shadowing within two classes of conservative flows: the incompressible and the Hamiltonian ones. We obtain that the first two properties guarantee dominated splitting (or partial hyperbolicity) on the whole manifold, and the third one implies that the flow is Anosov.

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Hyperbolicity and types of shadowing for $C^1$ generic vector fields

Cited by 13 publications

References 31 publications

Shadowing, expansiveness and specification for C1-conservative systems

Shadowing, expansiveness and specification for C1-conservative systems

Expansiveness, Shadowing and Markov Partition for Anosov Families

Conservative flows with various types of shadowing

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