The PIM-simplex method: an extension of the PIM-triple method to saddles with an arbitrary number of expanding directions
type: Item
instance of: scholarly article
title: The PIM-simplex method: an extension of the PIM-triple method to saddles with an arbitrary number of expanding directions
zbMATH Open document ID: 0955.37055
DOI: 10.1016/S0167-2789(98)00234-6
author: Pablo Moresco
author: Silvina Ponce Dawson
published in: Physica D
publication date: 1999-12-06T00:00:00Z
review text: The authors deal with the PIM-simplex method, which is a natural generalization of the PIM-triple method. Note that the PIM-triple method is a very good tool to obtain trajectories on saddles with one positive Lyapunov exponent. This paper is devoted to the cases when the PIM-triple method fails in saddles with several expanding directions and develop the modifications for new cases. Applications of the obtained results are discussed.
Mathematics Subject Classification ID: 37M99
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 65P20
zbMATH DE Number: 1374321
zbMATH Keywords: PIM-simplex method
zbMATH Keywords: PIM-triple method
zbMATH Keywords: saddles
zbMATH Keywords: Lyapunov exponent
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Q3135098
cites work: Transient chaos as the backbone of dynamics on strange attractors beyond crisis
cites work: A procedure for finding numerical trajectories on chaotic saddles
cites work: Analysis of a procedure for finding numerical trajectories close to chaotic saddle hyperbolic sets
cites work: A numerical procedure for finding accessible trajectories on basin boundaries
cites work: Q4003073
cites work: A Simplex Method for Function Minimization
cites work: Q5287558
cites work: Controlling chaotic dynamical systems
cites work: Spatiotemporal chaos in terms of unstable recurrent patterns
Wikidata QID: Q127753922
description: scientific article; zbMATH DE number 1374321