Dynamics MOC

Invariant set

In a dynamical system an invariant set is a subset of the phase space closed under time evolution, i.e. for all and all ¹. #m/def/dynamics

• A positively invariant set is invariant under forward evolution
• A negatively invariant set is invariant under reverse evolution

Examples

• Fixed point
• Every trajectory is an invariant set
• Separatrix
• Basin of attraction
• Constant manifold for a Conserved quantity
• - and -limit sets

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