nonwandering set

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Axiom A — In mathematics, Smale s axiom A defines a class of dynamical systems which have been extensively studied and whose dynamics is relatively well understood. A prominent example is the Smale horseshoe map. The term axiom A originates with Stephen… … Wikipedia
Anosov diffeomorphism — In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold M is a certain type of mapping, from M to itself, with rather clearly marked local directions of expansion and contraction .… … Wikipedia
Recurrent point — In mathematics, a recurrent point for function f is a point that is in the limit set of the iterated function f . Any neighborhood containing the recurrent point will also contain (a countable number of) iterates of it as well. DefinitionLet X be … Wikipedia
Pugh's closing lemma — In mathematics, Pugh s closing lemma is a result that links periodic orbit solutions of differential equations to chaotic behaviour. It can be formally stated as follows::Let f:M mapsto M be a C^1 diffeomorphism of a compact smooth manifold M .… … Wikipedia

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