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

  title={A connecting lemma for rational maps satisfying a no-growth condition},
  author={Juan 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… 
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