The topology of fluid flow past a sequence of cylinders

Judy Kennedy, Miguel A. F. Sanjuan, James A. Yorke, Celso Grebogi

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

This paper analyzes conditions under which dynamical systems in the plane have indecomposable continue or even infinite nested families of indecomposable continua. Our hypotheses are patterned after a numerical study of a fluid flow example, but should hold in a wide variety of physical processes. The basic fluid flow model is a differential equation in R-2 which is periodic in time, and so its solutions can be represented by a time-1 map F:R-2 --> R-2. We represent a version of this system "with noise" by considering any sequence of maps Fn:R-2 --> R-2, each of which is epsilon-close to F in the C-1 norm, so that if p is a point in the fluid flow at time n, then F-n(p) is its position at time n + 1. We show that indecomposable continua still exist for small epsilon. (C) 1999 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)207-242
Number of pages36
JournalTopology and its Applications
Volume94
Issue number1-3
Early online date25 May 1999
DOIs
Publication statusPublished - 9 Jun 1999

Keywords

  • indecomposable continua
  • horseshoes
  • fluid flow
  • noisy dynamical system
  • Lagrangian dynamics
  • area-preserving

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