Axiom A

Let M be a smooth manifoldMathworldPlanetmath. We say that a diffeomorphism f:MM satisfies (Smale’s) Axiom A (or that f is an Axiom A diffeomorphism) if

  1. 1.
  2. 2.

    the set of periodic points of f is dense in Ω(f): Per(f)¯=Ω(f).

Sometimes, Axiom A diffeomorphisms are called hyperbolic diffeomorphisms, because the portion of M where the “interesting” dynamics occur (namely, Ω(f)) has a hyperbolic behaviour.

Title Axiom A
Canonical name AxiomA
Date of creation 2013-03-22 13:40:27
Last modified on 2013-03-22 13:40:27
Owner Koro (127)
Last modified by Koro (127)
Numerical id 7
Author Koro (127)
Entry type Definition
Classification msc 37D20
Synonym hyperbolic diffeomorphism