Continuum-wise expansive homoclinic classes for robust dynamical systems

In the study, we consider continuum-wise expansiveness for the homoclinic class of a kind of $C^{1}$ -robustly expansive dynamical system. First, we show that if the homoclinic class $H(p, f)$ , which contains a hyperbolic periodic point p, is R-robustly continuum-wise expansive, then it is hyperbolic. For a vector field, if the homoclinic class $H(\gamma , X)$ does not include singularities and is R-robustly continuum-wise expansive, then it is hyperbolic.

Abstract licence: CC BY

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