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

The growing interest in non-attracting chaotic sets of high-dimensional dyn amical systems requires the development of numerical techniques for their s tudy. The PIM-triple method [H.E. Nusse, J.A. Yorke, Physica D 36 (1989) 13 7] is a very good method to obtain trajectories on saddles with one positiv e Lyapunov exponent. In this paper, we combine the same ideas with an algor ithm for finding local extrema of multi-variable functions to develop an ex tension of the method (the PIM-simplex method) that is suitable for the stu dy of sets with an arbitrary number of expanding directions. (C) 1999 Elsev ier Science B.V. All rights reserved.