### 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 language | English |
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Pages (from-to) | 207-242 |

Number of pages | 36 |

Journal | Topology and its Applications |

Volume | 94 |

Issue number | 1-3 |

Early online date | 25 May 1999 |

DOIs | |

Publication status | Published - 9 Jun 1999 |

### Keywords

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

## Cite this

*Topology and its Applications*,

*94*(1-3), 207-242. https://doi.org/10.1016/S0166-8641(98)00032-7