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Ming-Chia Li

  1. Covering relations for coupled map networks.

    Пнд, 09/12/2011 - 15:01 — SomNambul
    Authors: Leonid Bunimovich, Ming-Chia Li, Ming-Jiea Lyu
    Subjects: Dynamical Systems
    Abstract

    Following [6,12], we study coupled map networks over arbitrary finite graphs.
    An estimate from below for a topological entropy of a perturbed coupled map
    network via a topological entropy of an unperturbed network by making use of
    the covering relations for coupled map networks is obtained. The result is
    quite general, particularly no assumptions on hyperbolicity of a local dynamics
    or linearity of coupling are made.

  2. Coexistence of invariant sets with and without SRB measures in H\'enon family.

    Пнд, 07/12/2010 - 15:01 — SomNambul
    Authors: Teruhiko Soma, Shin Kiriki, Ming-Chia Li
    Subjects: Dynamical Systems
    Abstract

    Let $\{f_{a,b}\}$ be the (original) H\'enon family. In this paper, we show
    that, for any $b$ near $0$, there exists a closed interval $J_b$ which contains
    a dense subset $J'$ such that, for any $a\in J'$, $f_{a,b}$ has a quadratic
    homoclinic tangency associated with a saddle fixed point of $f_{a,b}$ which
    unfolds generically with respect to the one-parameter family $\{f_{a,b}\}_{a\in
    J_b}$. By applying this result, we prove that $J_b$ contains a residual subset
    $A_b^{(2)}$ such that, for any $a\in A_b^{(2)}$, $f_{a,b}$ admits the Newhouse
    phenomenon.

Math-arch

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