Lyapunov spectrum for Hénon-like maps at the first bifurcation

Research output: Contribution to journalArticle

Abstract

For a strongly dissipative Hénon-like map at the first bifurcation parameter at which the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set, we effect a multifractal analysis, i.e. decompose the set of non-wandering points on the unstable manifold into level sets of an unstable Lyapunov exponent, and give a partial description of the Lyapunov spectrum which encodes this decomposition. We derive a formula for the Hausdorff dimension of the level sets in terms of the entropy and unstable Lyapunov exponent of invariant probability measures, and show the continuity of the Lyapunov spectrum. We also show that the set of points for which the unstable Lyapunov exponents do not exist carries the full Hausdorff dimension.

Original languageEnglish
Pages (from-to)1-33
Number of pages33
JournalErgodic Theory and Dynamical Systems
DOIs
Publication statusAccepted/In press - 2016 Nov 10

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Lyapunov Spectrum
Lyapunov Exponent
Entropy
Bifurcation
Unstable
Decomposition
Hausdorff Dimension
Level Set
Decompose
Multifractal Analysis
Unstable Manifold
Limit Set
Hyperbolicity
Invariant Measure
Set of points
Probability Measure
Partial

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Lyapunov spectrum for Hénon-like maps at the first bifurcation. / Takahasi, Hiroki.

In: Ergodic Theory and Dynamical Systems, 10.11.2016, p. 1-33.

Research output: Contribution to journalArticle

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