Vector Fields with the Asymptotic Orbital Pseudo-orbit Tracing Property

Lee, Manseob; Park, Junmi

doi:10.1007/s12346-020-00388-z

Cited by 2 publications

(1 citation statement)

References 28 publications

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“…41-53 2 computations in dynamics systems in [2], [3], [4]and [5]. The answer about of this problem, researchers used several types of shadowing property for proof hyperbolic, see [6], [7], [8], [9]and [10].…”

Section: Introductionmentioning

confidence: 99%

Eventual Fitting Shadowing Property for Hyperbolic Dynamical Systems

AL-Ftlawy,

AL-Shara

2023

JQCM

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Let be a diffeomorphism map on a closed smooth manifold for dimension . We explain in this work any chain transitive set of generic diffeomorphism , if a diffeomorphism has another type of shadowing property is called, the eventual shadowing property on locally maximal chain transitive set, then is hyperbolic. In general, the eventual fitting shadowing property is not fulfilled in hyperbolic dynamical systems (satisfy in case L is Anosov diffeomorphism map) . In this paper, several concepts were presented. These concepts can be re-examined on other important spaces, and their impact on finding dynamical characteristics that may be employed in solving some mathematical problems.

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Section: Introductionmentioning

confidence: 99%

Eventual Fitting Shadowing Property for Hyperbolic Dynamical Systems

AL-Ftlawy,

AL-Shara

2023

JQCM

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Flows with ergodic pseudo orbit tracing property

Lee

2022

era

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<abstract><p>In the manuscript, we deal with a type of pseudo orbit tracing property and hyperbolicity about a vector field (or a divergence free vector field). We prove that a vector field (or a divergence free vector field) of a smooth closed manifold $ M $ has the robustly ergodic pseudo orbit tracing property then it does not contain any singularities and it is Anosov. Additionally, there is a dense and open set $ \mathcal{R} $ in the set of $ C^1 $ a vector field (or a divergence free vector field) of a smooth closed manifold $ M $ such that given a vector field (or a divergence free vector field) has the ergodic pseudo orbit tracing property then it does not contain singularities and it is Anosov.</p></abstract>

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Vector Fields with the Asymptotic Orbital Pseudo-orbit Tracing Property

Cited by 2 publications

References 28 publications

Eventual Fitting Shadowing Property for Hyperbolic Dynamical Systems

Eventual Fitting Shadowing Property for Hyperbolic Dynamical Systems

Flows with ergodic pseudo orbit tracing property

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