On stability of forcing relations for multidimensional perturbations of interval maps

Ming-Chia Li; Piotr Zgliczyński

doi:10.4064/fm206-0-13

On stability of forcing relations for multidimensional perturbations of interval maps

Ming-Chia Li^*, Piotr Zgliczyński

^*Corresponding author for this work

National Chiao Tung University

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

Abstract

We show that all periods of periodic points forced by a pattern for interval maps are preserved for high-dimensional maps if the multidimensional perturbation is small. We also show that if an interval map has a fixed point associated with a homoclinic-like orbit then any small multidimensional perturbation has periodic points of all periods.

Original language	English
Pages (from-to)	241-251
Number of pages	11
Journal	Fundamenta Mathematicae
Volume	206
Issue number	1
DOIs	https://doi.org/10.4064/fm206-0-13
State	Published - 1 Jan 2009

Keywords

Covering relations
Forcing relations
Multidimensional perturbation
Patterns

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AB - We show that all periods of periodic points forced by a pattern for interval maps are preserved for high-dimensional maps if the multidimensional perturbation is small. We also show that if an interval map has a fixed point associated with a homoclinic-like orbit then any small multidimensional perturbation has periodic points of all periods.

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KW - Patterns

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On stability of forcing relations for multidimensional perturbations of interval maps

Abstract

Keywords

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