Bounded nonwandering sets for polynomial mappings

Ming-Chia Li*, M. Malkin

*Corresponding author for this work

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

In this paper, we consider a class of polynomial mappings on ℝm or ℂm which is defined by the assumption that the delay equations induced by the mappings have leading monomials in a single variable. We show that for any mapping from this class, the nonwandering set is bounded while for all unbounded orbits, some kind of monotonicity takes place. The class under consideration is proved to contain, in particular, the generalized Hénon mappings and the Arneodo-Coullet-Tresser mappings.

Original languageEnglish
Pages (from-to)377-389
Number of pages13
JournalJournal of Dynamical and Control Systems
Volume10
Issue number3
DOIs
StatePublished - 1 Jul 2004

Keywords

  • Generalized Hénon mappings
  • Nonwandering points
  • Polynomial mappings
  • Topological entropy
  • Unbounded orbits

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