Renormalisable Henon-like Maps and Unbounded Geometry

Details Renormalisable Henon-like Maps and Unbounded Geometry Renormalisable Henon-like Maps and Unbounded Geometry

2010-02-22

arxiv.org/abs/1002.3942v1

Mathematics

Dynamical Systems

29 pages, 2 figures

Scientific paper

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.

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