PlanetMath: homoclinic

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homoclinic

(Definition)

If is a topological space and is a flow on or an homeomorphism mapping to itself, we say that $x\in X$ is an homoclinic point (or homoclinic intersection) if it belongs to both the stable and unstable sets of some fixed or periodic point ; i.e.

$\displaystyle x\in W^s(f,p)\cap W^u(f,p).$

The orbit of an homoclinic point is called an homoclinic orbit.

"homoclinic" is owned by Koro.

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Cross-references: orbit, periodic point, fixed, unstable sets, stable, intersection, point, mapping, homeomorphism, flow, topological space
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This is version 2 of homoclinic, born on 2003-07-29, modified 2003-07-29.
Object id is 4532, canonical name is Homoclinic.
Accessed 2771 times total.

Classification:

37C29 (Dynamical systems and ergodic theory :: Smooth dynamical systems: general theory :: Homoclinic and heteroclinic orbits)

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