hyperbolic fixed point
Let be a smooth manifold. A fixed point of a diffeomorphism is said to be a hyperbolic fixed point if is a linear hyperbolic isomorphism. If is a periodic point of least period , it is called a hyperbolic periodic point if it is a hyperbolic fixed point of (the -th iterate of ).
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 |