be a system of autonomousMathworldPlanetmath ordinary differential equationMathworldPlanetmath in n defined by a vector field f:nn. A set A is said to be an attracting set[GH, P] if

  1. 1.

    A is closed and invariant,

  2. 2.

    there exists an open neighborhood U of A such that all solution with initial solution in U will eventually enter A (x(t)A) as t.

Additionally, if A contains a dense orbit then A is said to be an attractor[GH, P].
Conversely, a set R is said to be a repelling set[GH] if R satisfy the condition 1. and 2. where t is replaced by t-. Similarly, if R contains a dense orbit then R is said to be a repellor[GH].


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