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

PHYSICA D - NONLINEAR PHENOMENA

Año: 1999 vol. 126 p. 38 - 48

0167-2789

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.