Using Horseshoes to Create Coherent Structures

Details Using Horseshoes to Create Coherent Structures Using Horseshoes to Create Coherent Structures

1993-06-24

arxiv.org/abs/chao-dyn/9306010v1

Nonlinear Sciences

Chaotic Dynamics

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Scientific paper

In this letter, we show that coherent structures are related to folds of horseshoes which are present in chaotic systems. We develop techniques that allow us to construct coherent structures by manipulating folds in three prototypical problems: a 1-D chaotic map, a 2-D chaotic map, and a chaotically advected fluid. The ability to construct such structures is of practical importance for the control of chaotic or turbulent extended systems such as fluids, plasmas, and coupled oscillator arrays.

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