Properties
Any Anosov diffeomorphism satisfies axiom A. In this case, the whole manifold M is hyperbolic (although it is an open question whether the non-wandering set Ω(f) constitutes the whole M).
Rufus Bowen showed that the non-wandering set Ω(f) of any axiom A diffeomorphism supports a Markov partition. Thus the restriction of f to a certain generic subset of Ω(f) is conjugated to a shift of finite type.
The density of the periodic points in the non-wandering set implies its local maximality: there exists an open neighborhood U of Ω(f) such that
Read more about this topic: Axiom A
Famous quotes containing the word properties:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)