Renormalizable Hénon-like maps and unbounded geometry

P. E. Hazard; M. Lyubich; M. Martens

doi:10.1088/0951-7715/25/2/397

Renormalizable Hénon-like maps and unbounded geometry

P. E. Hazard
, M. Lyubich
, M. Martens

University of Warwick

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We show that given a one-parameter family F _b of strongly dissipative infinitely renormalizable Hénon-like maps, parametrized 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.

Original language	English
Pages (from-to)	397-420
Number of pages	24
Journal	Nonlinearity
Volume	25
Issue number	2
DOIs	https://doi.org/10.1088/0951-7715/25/2/397
State	Published - Feb 2012

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abstract = "We show that given a one-parameter family F b of strongly dissipative infinitely renormalizable H{\'e}non-like maps, parametrized 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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AU - Martens, M.

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N2 - We show that given a one-parameter family F b of strongly dissipative infinitely renormalizable Hénon-like maps, parametrized 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.

AB - We show that given a one-parameter family F b of strongly dissipative infinitely renormalizable Hénon-like maps, parametrized 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.

UR - https://www.scopus.com/pages/publications/84856191697

U2 - 10.1088/0951-7715/25/2/397

DO - 10.1088/0951-7715/25/2/397

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VL - 25

SP - 397

EP - 420

JO - Nonlinearity

JF - Nonlinearity

IS - 2

ER -

Renormalizable Hénon-like maps and unbounded geometry

Abstract

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