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ENTROPY, POSITIVELY CONTINUUM-WISE EXPANSIVENESS AND SHADOWING
이만섭,박준미 충청수학회 2015 충청수학회지 Vol.28 No.4
Let (X; d) be a compact metric space, and let f : X ! X be a continuous map. We consider that if a positively continuum- wise expansiveness continuous map f has the positively shadowing property in the nonwandering set, then the topological entropy is positive.
ASYMPTOTIC AVERAGE SHADOWING PROPERTY ON A CLOSED SET
이만섭,박준미 충청수학회 2012 충청수학회지 Vol.25 No.1
Let $f$ be a difeomorphism of a closed $n$-dimensional smooth manifold $M,$ and $p$ be a hyperbolic periodic point of $f.$ Let $\Lambda(p)$ be a closed set which containing $p.$ In this paper, we show that (i) if $f$ has the asymptotic average shadowing property on $\Lambda(p),$ then $\Lambda(p)$ is the chain component which contains $p.$ (ii) suppose $f$ has the asymptotic average shadowing property on $\Lambda(p).$ Then if $f|_{\Lambda(p)}$ has the $C^1$-stably shadowing property then it is hyperbolic.
Robustly chain transitive sets with shadowing
이만섭,박준미 충청수학회 2013 충청수학회지 Vol.26 No.4
Let f be a diffeomorphism of a closed C∞ manifold M, and let ∧ ⊂ M be a closed f-invariant set. We show that if f|∧ is robustly chain transitive with shadowing, then ¤ is the hyperbolic homoclinic class.
PERIODICAL EXPANSIVENESS FOR C1-GENERIC DIFFEOMORPHISMS
안지원,이승희,박준미 충청수학회 2015 충청수학회지 Vol.28 No.3
C1-generically, if a transitive di®eomorphism f is pe- riodically expansive, then it is hyperbolic.
LIMIT SHADOWING WITH C⁰ TRANSVERSALITY CONDITION
이건희,이만섭,박준미 충청수학회 2012 충청수학회지 Vol.25 No.2
Let f be an Axiom A difeomorphism of a closed 2-dimensional smooth manifold M: We show that f has the limit shadowing property if and only if f satiss the C⁰transversality condition.
Shadowable chain components and hyperbolicity
이만섭,이승희,박준미 대한수학회 2015 대한수학회보 Vol.52 No.1
We show that $C^1$-generically, the shadowable chain component of a $C^1$-vector field containing a hyperbolic periodic orbit is hyperbolic if it is locally maximal.
Linear diffeomorphisms with limit shadowing
이건희,이만섭,박준미 충청수학회 2013 충청수학회지 Vol.26 No.2
In this paper, we show that for a linear dynamical sys-tem f(x) = Ax of Cn, f has the limit shadowing property if and only if the matrix A is hyperbolic. In this paper, we show that for a linear dynamical system f(x) = Ax of Cn, f has the limit shadowing property if and only if the matrix A is hyperbolic.
UNIVERSALLY MEASURE CONTINUUM-WISE EXPANSIVE HOMOCLINIC CLASSES
이승희,김대정,박준미 충청수학회 2023 충청수학회지 Vol.36 No.3
Investigating local dynamics requires precise controlto effectively manage the subtle differences that distinguish it fromglobal dynamics. This paper aims to study the localized perspectiveof the recently proposed continuum-wise expansive measures [13]. Let f : M → M be a diffeomorphism on a closed smooth manifoldM and let p be a hyperbolic periodic point of f. We prove thatif the homoclinic class Hf (p) of f associated to p is C1-robustlymeasure continuum-wise expansive then it is hyperbolic.