Birkhoff spectrum for Hénon-like maps at the first bifurcation

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Abstract

We effect a multifractal analysis 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 decompose the set of non-wandering points on the unstable manifold into level sets of Birkhoff averages of continuous functions, and derive a formula for the Hausdorff dimension of the level sets in terms of the entropy and unstable Lyapunov exponent of invariant probability measures.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalDynamical Systems
DOIs
Publication statusAccepted/In press - 2015 Nov 1

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Keywords

  • first bifurcation
  • hénon-like map
  • multifractal analysis
  • non hyperbolicity

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications

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