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 language | English |
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Pages (from-to) | 38-48 |
Number of pages | 11 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 126 |
Issue number | 1-2 |
DOIs | |
State | Published - Feb 1 1999 |
Externally published | Yes |
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