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

3 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 language	English
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
Publication status	Published - 2012 Feb
Externally published	Yes

ASJC Scopus subject areas

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

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10.1088/0951-7715/25/2/533

Cite this

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

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.",

author = "Hiroki Takahasi and Qiudong Wang",

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AU - Takahasi, Hiroki

AU - Wang, Qiudong

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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.

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

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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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