hyperbolic fixed point

Let $M$ be a smooth manifold. A fixed point $x$ of a diffeomorphism$f:M\to M$ is said to be a hyperbolic fixed point if $Df(x)$ is a linear hyperbolic isomorphism. If $x$ is a periodic point of least period $n$, it is called a hyperbolic periodic point if it is a hyperbolic fixed point of $f^n$ (the $n$-th iterate of $f$).

If the dimension of the stable manifold of a fixed point is zero, the point is called a source; if the dimension of its unstable manifold is zero, it is called a sink; and if both the stable and unstable manifold have nonzero dimension, it is called a saddle.

Title	hyperbolic fixed point
Canonical name	HyperbolicFixedPoint
Date of creation	2013-03-22 13:47:57
Last modified on	2013-03-22 13:47:57
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	6
Author	Koro (127)
Entry type	Definition
Classification	msc 37C25
Classification	msc 37D05
Related topic	StableManifold
Related topic	HyperbolicSet
Defines	hyperbolic periodic point
Defines	source
Defines	sink
Defines	saddle