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18 results on '"Park, Junmi"'

1. Kinematic N-expansive flows

Author

Lee, Manseob, Oh, Jumi, and Park, Junmi

Subjects
Mathematics - Dynamical Systems, 37C20, 37C05, 37C29, 37D05
Abstract

In light of the rich results of expansiveness in the dynamics of diffeomorphisms, it is natural to consider another notions of expansiveness such as countably-expansive, measure expansive, $N$-expansive and so on. In this paper, we introduce the notion of $N$-expansiveness for flows on a $C^{\infty}$ compact connected Riemannian manifold by using the kinematic expansiveness which is extension of the $N$-expansive diffeomorphisms. And we prove that a vector field $X$ on $M$ is $C^1$ robustly kinematic $N$-expansive then $X$ satisfies quasi-Anosov. Furthermore, we consider the hyperbolicity of local dynamical systems with kinematic $N$-expansiveness., Comment: 14 page

Published
2018

9. Expansive transitive sets for robust and generic diffeomorphisms.

Author

Lee, Manseob and Park, Junmi

Subjects
*DIFFEOMORPHISMS, *RIEMANNIAN manifolds, *HYPERBOLIC geometry, *MULTIPLY transitive groups, *MANIFOLDS (Mathematics)
Abstract

Let f be a diffeomorphism on a compact smooth Riemannian manifold M, and let Λ be a closed f-invariant transitive subset of M. In this paper, we show that f|Λ is C1-stably expansive if and only if Λ is a hyperbolic basic set. Moreover, C1-generically, a locally maximal transitive set Λ is expansive if and only if it is a hyperbolic basic set. [ABSTRACT FROM AUTHOR]

Published
2018
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13. Expansive homoclinic classes of generic C -vector fields.

Author

Lee, Seunghee and Park, Junmi

Subjects
VECTOR fields, ALGEBRAIC field theory, HYPERBOLIC differential equations, PARTIAL differential equations, HYPERBOLIC functions
Abstract

Let γ be a hyperbolic closed orbit of a C vector field X on a compact C manifold M of dimension n ≥ 3, and let H (γ) be the homoclinic class of X containing γ. In this paper, we prove that C -generically, if H (γ) is expansive and isolated, then it is hyperbolic. [ABSTRACT FROM AUTHOR]

Published
2016
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18. C2-Stably Limit Shadowing Diffeomorphisms.

Author

Lee, Manseob and Park, Junmi

Subjects
*DIFFEOMORPHISMS, *LIMITS (Mathematics), *SHADOWING theorem (Mathematics), *AXIOMS, *MATHEMATICAL analysis
Abstract

Let f be a diffeomorphism on a C∞ closed surface. In this paper, we show that if f has the C2-stably limit shadowing property, then we have the following: (i) f satisfies the Kupka-Smale condition; (ii) if P(f) is dense in the nonwandering set Ω(f) and if there is a dominated splitting on Ps(f), then f satisfies both Axiom A and the strong transversality condition. [ABSTRACT FROM AUTHOR]

Published
2015
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