Hyperbolic models for transitive topological Anosov flows in dimension three

Shannon, Mario

doi:10.48550/arxiv.2108.12000

Cited by 2 publications

(2 citation statements)

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“…It has been a long standing problem to determine whether in general every topological Anosov flow is orbit equivalent to an Anosov flow. Just recently in [26] every transitive topological Anosov flow in dimension 3 (for a more general definition of topological Anosov flow that covers Definition 3.13) has been shown to be orbit equivalent to a smooth Anosov flow.…”

Section: Uniqueness Of Invariant Foliationsmentioning

confidence: 99%

Global stability of discretized Anosov flows

Martinchich¹

2023

JMD

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The goal of this article is to establish several general properties of a somewhat large class of partially hyperbolic diffeomorphisms called discretized Anosov flows. A general definition for these systems is presented and is proven to be equivalent with the definition introduced in [1], as well as with the notion of flow type partially hyperbolic diffeomorphisms introduced in [13].The set of discretized Anosov flows is shown to be C 1 -open and closed inside the set of partially hyperbolic diffeomorphisms. Every discretized Anosov flow is proven to be dynamically coherent and plaque expansive. Unique integrability of the center bundle is shown to happen for whole connected components, notably the ones containing the time 1 map of an Anosov flow. For general connected components, a result on uniqueness of invariant foliation is obtained.Similar results are seen to happen for partially hyperbolic systems admitting a uniformly compact center foliation extending the studies initiated in [6].

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Section: Uniqueness Of Invariant Foliationsmentioning

confidence: 99%

Global stability of discretized Anosov flows

Martinchich¹

2023

JMD

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“…It is worth noting that Definition 3.1 is strictly more restrictive than other definitions of topological Anosov flows appearing in the literature since we are asking for Bϕt Bt | t"0 to be a continuous vector field. Recently in [Sh21] every transitive topological Anosov flow in dimension 3 (for a more general definition of topological Anosov flow that covers Definition 3.1) has been shown to be orbit equivalent to a smooth Anosov flow.…”

Section: Suppose W Csmentioning

confidence: 99%

Global stability of discretized Anosov flows

Martinchich¹

2022

Preprint

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The goal of this article is to establish several general properties of a somewhat large class of partially hyperbolic diffeomorphisms called discretized Anosov flows. A general definition for these systems is presented and is proven to be equivalent with the definition introduced in [BFFP19], as well as with the notion of flow type partially hyperbolic diffeomorphisms introduced in [BFT20].The set of discretized Anosov flows is shown to be C 1 open and closed inside the set of partially hyperbolic diffeomorphisms. Every discretized Anosov flow is proven to be dynamically coherent and plaque expansive. Unique integrability of the center bundle is shown to happen for whole connected components, notably the ones containing the time 1 map of an Anosov flow. For general connected components, a result on uniqueness of invariant foliation is obtained.Similar results are seen to happen for partially hyperbolic systems admitting a uniformly compact center foliation extending the studies initiated in [BB16].

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Hyperbolic models for transitive topological Anosov flows in dimension three

Abstract: We prove that every transitive topological Anosov flow on a closed 3-manifold is orbitally equivalent to a smooth Anosov flow, preserving an ergodic smooth volume form. ContentsIntroduction.

Cited by 2 publications

References 19 publications

Global stability of discretized Anosov flows

Global stability of discretized Anosov flows

Global stability of discretized Anosov flows

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