Nonuniformly expanding 1D maps with logarithmic singularities

Hiroki Takahasi; Qiudong Wang

doi:10.1088/0951-7715/25/2/533

Nonuniformly expanding 1D maps with logarithmic singularities

Hiroki Takahasi, Qiudong Wang

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

4 Scopus citations

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 language	English (US)
Pages (from-to)	533-550
Number of pages	18
Journal	Nonlinearity
Volume	25
Issue number	2
DOIs	https://doi.org/10.1088/0951-7715/25/2/533
State	Published - Feb 2012

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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10.1088/0951-7715/25/2/533

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title = "Nonuniformly expanding 1D maps with logarithmic singularities",

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T1 - Nonuniformly expanding 1D maps with logarithmic singularities

AU - Takahasi, Hiroki

AU - Wang, Qiudong

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N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/84862908280

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U2 - 10.1088/0951-7715/25/2/533

DO - 10.1088/0951-7715/25/2/533

M3 - Article

AN - SCOPUS:84862908280

SN - 0951-7715

VL - 25

SP - 533

EP - 550

JO - Nonlinearity

JF - Nonlinearity

IS - 2

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Nonuniformly expanding 1D maps with logarithmic singularities

Abstract

ASJC Scopus subject areas

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