A connecting lemma for rational maps satisfying a no-growth condition

  title={A connecting lemma for rational maps satisfying a no-growth condition},
  author={J. Rivera-Letelier},
  journal={Ergodic Theory and Dynamical Systems},
  pages={595 - 636}
We introduce and study a non-uniform hyperbolicity condition for complex rational maps that does not involve a growth condition. We call this condition backward contraction. We show this condition is weaker than the Collet–Eckmann condition, and than the summability condition with exponent one. Our main result is a connecting lemma for backward-contracting rational maps, roughly saying that we can perturb a rational map to connect each critical orbit in the Julia set with an orbit that does not… Expand
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  • N. Dobbs
  • Mathematics
  • Mathematical Proceedings of the Cambridge Philosophical Society
  • 2010