The PIM-simplex method: An extension of the PIM-triple method to saddles with an arbitrary number of expanding directions

Pablo Moresco, Silvina Ponce Dawson

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21 Scopus citations

Abstract

The growing interest in non-attracting chaotic sets of high-dimensional dynamical systems requires the development of numerical techniques for their study. The PIM-triple method [H.E. Nusse, J.A. Yorke, Physica D 36 (1989) 137] is a very good method to obtain trajectories on saddles with one positive Lyapunov exponent. In this paper, we combine the same ideas with an algorithm for finding local extrema of multi-variable functions to develop an extension of the method (the PIM-simplex method) that is suitable for the study of sets with an arbitrary number of expanding directions.

Original languageEnglish
Pages (from-to)38-48
Number of pages11
JournalPhysica D: Nonlinear Phenomena
Volume126
Issue number1-2
DOIs
StatePublished - Feb 1 1999
Externally publishedYes

Funding

This work was supported by the University of Buenos Aires, CONICET and Fundación Antorchas. We acknowledge useful conversations with Gabriel Mindlin and Jim Yorke.

Keywords

  • 02.70.-c
  • 05.45.+b
  • Algorithm
  • Dynamics
  • Method
  • Saddle

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