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Analysis of a procedure for finding numerical trajectories close to chaotic saddle hyperbolic sets†

Published online by Cambridge University Press:  19 September 2008

Helena E. Nusse  and
James A. Yorke
Helena E. Nusse
Affiliation:
University of Maryland, College Park, Maryland 20742, USA
James A. Yorke
Affiliation:
University of Maryland, College Park, Maryland 20742, USA
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Abstract

In dynamical systems examples are common in which there are regions containing chaotic sets that are not attractors, e.g. systems with horseshoes have such regions. In such dynamical systems one will observe chaotic transients. An important problem is the ‘Dynamical Restraint Problem’: given a region that contains a chaotic set but contains no attractor, find a chaotic trajectory numerically that remains in the region for an arbitrarily long period of time.

We present two procedures (‘PIM triple procedures’) for finding trajectories which stay extremely close to such chaotic sets for arbitrarily long periods of time.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 1 , March 1991 , pp. 189 - 208
Copyright
Copyright © Cambridge University Press 1991

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