Nonuniformly expanding 1D maps with logarithmic singularities

Hiroki Takahasi, Qiudong Wang

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

For a certain parametrized family of maps on a circle with critical points and logarithmic singularities where derivatives blow up to infinity, we construct a positive measure set of parameters corresponding to maps which exhibit nonuniformly expanding behaviour. This implies the existence of "chaotic" dynamics in dissipative homoclinic tangles in periodically perturbed differential equations.

Original languageEnglish
Pages (from-to)533-550
Number of pages18
JournalNonlinearity
Volume25
Issue number2
DOIs
Publication statusPublished - 2012 Feb
Externally publishedYes

Fingerprint

Expanding Maps
Logarithmic
Singularity
Tangles
Homoclinic
Chaotic Dynamics
infinity
Blow-up
Critical point
critical point
Circle
Differential equations
differential equations
Infinity
Differential equation
Derivatives
Imply
Derivative
Family

ASJC Scopus subject areas

  • Applied Mathematics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Nonuniformly expanding 1D maps with logarithmic singularities. / Takahasi, Hiroki; Wang, Qiudong.

In: Nonlinearity, Vol. 25, No. 2, 02.2012, p. 533-550.

Research output: Contribution to journalArticle

Takahasi, Hiroki ; Wang, Qiudong. / Nonuniformly expanding 1D maps with logarithmic singularities. In: Nonlinearity. 2012 ; Vol. 25, No. 2. pp. 533-550.
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