Abstract
Abstract We show that for C 1 generic diffeomorphisms, an isolated homoclinic class is shadow-able if and only if it is a hyperbolic basic set. Mathematics Subject Classification 2000: 37C20; 37C05; 37C29; 37D05.
Highlights
Let M be a closed C∞ manifold, and denote by d the distance on M induced from the Riemannian metric ∥ · ∥ on the tangent bundle TM
Denote by Diff(M) the space of diffeo-morphisms of M endowed with the C1-topology
We say that two hyperbolic periodic points p and q are homoclinically related, and write p ~ q, if Ws(p) Wu(q) = ∅ and Wu(p) Ws(q) = ∅
Summary
Let M be a closed C∞ manifold, and denote by d the distance on M induced from the Riemannian metric ∥ · ∥ on the tangent bundle TM. We say that two hyperbolic periodic points p and q are homoclinically related, and write p ~ q, if Ws(p) Wu(q) = ∅ and Wu(p) Ws(q) = ∅.
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