Abstract
In this paper, we discuss the robustly chain transitive set, and show that the robustly chain transitive set is hyperbolic if and only if every periodic points in the set is hyperbolic and has the same index.
Highlights
In the theory of dynamical systems one has been to describe and characterize systems exhibiting dynamical properties that are preserved under small perturbations
Structurally stable systems and -stable systems have been the main objects of interests in the global qualitative theory of dynamical systems and they are characterized as the hyperbolic ones
We study the relation between the robustly chain transitive and hyperbolicity
Summary
In the theory of dynamical systems one has been to describe and characterize systems exhibiting dynamical properties that are preserved under small perturbations. Let f ∈ Diff(M) and be a closed f -invariant set. The set is transitive if there is a point x ∈ such that ω(x) = .
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