hyperbolic fixed point

Let M be a smooth manifoldMathworldPlanetmath. A fixed pointMathworldPlanetmath x of a diffeomorphism f:MM is said to be a hyperbolic fixed pointMathworldPlanetmath 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 fn (the n-th iterate of f).

If the dimensionMathworldPlanetmathPlanetmath 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