attractor
Let
be a system of autonomous ordinary differential equation in defined by a vector field . A set is said to be an attracting set[GH, P] if
-
1.
is closed and invariant,
-
2.
there exists an open neighborhood of such that all solution with initial solution in will eventually enter () as .
Additionally, if contains a dense orbit then is said to be an attractor[GH, P].
Conversely, a set is said to be a repelling set[GH] if satisfy the condition 1. and 2. where is replaced by . Similarly, if contains a dense orbit then is said to be a repellor[GH].
References
- GH Guckenheimer, John & Holmes, Philip, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, New York, 1983.
- P Perko, Lawrence, Differential Equations and Dynamical Systems, Springer, New York, 2001.
Title | attractor |
---|---|
Canonical name | Attractor |
Date of creation | 2013-03-22 15:17:34 |
Last modified on | 2013-03-22 15:17:34 |
Owner | Daume (40) |
Last modified by | Daume (40) |
Numerical id | 4 |
Author | Daume (40) |
Entry type | Definition |
Classification | msc 34C99 |
Defines | attracting set |
Defines | repelling set |
Defines | repellor |