All solenoids of piecewise smooth maps are period doubling

Lluís Alsedà, Víctor Jiménez López, L'ubomír Snoha

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

We show that piecewise smooth maps with a finite number of pieces of monotonicity and nowhere vanishing Lipschitz continuous derivative can have only period doubling solenoids. The proof is based on the fact that if p1 < ... < pn is a periodic orbit of a continuous map f then there is a union set {q1,..., qn-1} of some periodic orbits of f such that Pi < qi < Pi+i for any i.
Original languageEnglish
Pages (from-to)121-138
JournalFundamenta Mathematicae
Volume157
Issue number2-3
Publication statusPublished - 1 Dec 1998

Keywords

  • Markov graph
  • Periodic point
  • Piecewise linear map
  • Piecewise smooth map with nowhere vanishing Lipschitz continuous derivative
  • Solenoid

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