On stability of forcing relations for multidimensional perturbations of interval maps

Ming-Chia Li*, Piotr Zgliczyński

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)241-251
Number of pages11
JournalFundamenta Mathematicae
Volume206
Issue number1
DOIs
StatePublished - 1 Jan 2009

Keywords

  • Covering relations
  • Forcing relations
  • Multidimensional perturbation
  • Patterns

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