Renormalisable Henon-like Maps and Unbounded Geometry

Peter Hazard; Mikhail Lyubich; Marco Martens

Renormalisable Henon-like Maps and Unbounded Geometry

Dynamical Systems 2010-02-23 v1

Authors: Peter Hazard , Mikhail Lyubich , Marco Martens

Abstract

We show that given a one parameter family $F_b$ of strongly dissipative infinitely renormalisable H\'enon-like maps, parametrised by a quantity called the `average Jacobian' $b$ , the set of all parameters $b$ such that $F_b$ has a Cantor set with unbounded geometry has full Lebesgue measure.

Keywords

thurston maps

Cite

@article{arxiv.1002.3942,
  title  = {Renormalisable Henon-like Maps and Unbounded Geometry},
  author = {Peter Hazard and Mikhail Lyubich and Marco Martens},
  journal= {arXiv preprint arXiv:1002.3942},
  year   = {2010}
}

Comments

29 pages, 2 figures

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