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|
|Date of creation||2013-03-22 13:47:57|
|Last modified on||2013-03-22 13:47:57|
|Last modified by||Koro (127)|
|Defines||hyperbolic periodic point|