Birkhoff spectrum for Hénon-like maps at the first bifurcation

Research output: Contribution to journalArticle

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

Fingerprint

Level Set
Entropy
Bifurcation
Multifractal Analysis
Unstable Manifold
Limit Set
Hyperbolicity
Hausdorff Dimension
Invariant Measure
Lyapunov Exponent
Probability Measure
Continuous Function
Unstable
Decompose

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications

Cite this

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

In: Dynamical Systems, 01.11.2015, p. 1-19.

Research output: Contribution to journalArticle

@article{ea7e9ec55362474da55af69980e53ed8,
title = "Birkhoff spectrum for H{\'e}non-like maps at the first bifurcation",
abstract = "We effect a multifractal analysis for a strongly dissipative H{\'e}non-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.",
keywords = "first bifurcation, h{\'e}non-like map, multifractal analysis, non hyperbolicity",
author = "Hiroki Takahasi",
year = "2015",
month = "11",
day = "1",
doi = "10.1080/14689367.2015.1102201",
language = "English",
pages = "1--19",
journal = "Dynamical Systems",
issn = "1468-9367",
publisher = "Taylor and Francis Ltd.",

}

TY - JOUR

T1 - Birkhoff spectrum for Hénon-like maps at the first bifurcation

AU - Takahasi, Hiroki

PY - 2015/11/1

Y1 - 2015/11/1

N2 - 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.

AB - 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.

KW - first bifurcation

KW - hénon-like map

KW - multifractal analysis

KW - non hyperbolicity

UR - http://www.scopus.com/inward/record.url?scp=84947718557&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84947718557&partnerID=8YFLogxK

U2 - 10.1080/14689367.2015.1102201

DO - 10.1080/14689367.2015.1102201

M3 - Article

AN - SCOPUS:84947718557

SP - 1

EP - 19

JO - Dynamical Systems

JF - Dynamical Systems

SN - 1468-9367

ER -