As recalled by Wikipedia:

Although no universally accepted mathematical definition of chaos exists, a commonly used definition originally formulated by Robert L. Devaney says that, to classify a dynamical system as chaotic, it must have these properties:

  • it must be sensitive to initial conditions,
  • it must be topologically transitive
  • it must have dense periodic orbits.

I also know that a way to obtain chaos in phase space is when the system causes trajectories to stretch and fold. I would like to understand the connection between the stretching and folding process and the properties of aforementioned definition. The sensitivity to initial conditions is probably related to stretching dynamics but is the "folding" related to other two properties? And if yes, why?

Answers, books and articles are welcome. Thanks!


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