Invariant set

- and -limit sets

The -limit set (-limit set ) of is the set of all for which there exists a strictly increasing (decreasing), unbounded sequence of times such that .1 #m/def/dynamics

Properties

  1. If is bounded then is inhabited and connected
  2. If is closed then it contains its limit points
  3. is Invariant set
  4. and implies


#state/develop | #lang/en | #SemBr

Footnotes

  1. 2021. MATH3021: Nonlinear dynamics & chaos, pp. 54ff.