How to prune a horseshoe

@article{Carvalho2002HowTP,
  title={How to prune a horseshoe},
  author={A. D. Carvalho and Toby Hall},
  journal={Nonlinearity},
  year={2002},
  volume={15}
}
Let F : 2→2 be a homeomorphism. An open F-invariant subset U of 2 is a pruning region for F if it is possible to deform F continuously to a homeomorphism FU for which every point of U is wandering, but which has the same dynamics as F outside of U. This concept is motivated by the Pruning Front Conjecture (PFC) introduced by Cvitanovic, which claims that every Henon map can be understood as a pruned horseshoe. This paper contains recent results in pruning theory, concentrating on prunings of… Expand
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