Existence and computation of hyperbolic trajectories of aperiodically time dependent vector fields and their approximations

N Ju, DM Small, SR Wiggins

Research output: Contribution to journalArticle (Academic Journal)peer-review

30 Citations (Scopus)

Abstract

In this paper we give sufficient conditions for the existence of hyperbolic trajectories in aperiodically time dependent vector fields. These conditions do not require the a priori introduction of hyperbolicity into the dynamics of the vector field or assumptions of "time scale separation". The hyperbolic trajectory is obtained as a solution of an integral equation over an infinite time interval. We give an expression for the error obtained when the solution is approximated over a finite time interval. Finally, we show how the method can be numerically implemented in a specific example.
Translated title of the contributionExistence and computation of hyperbolic trajectories of aperiodically time dependent vector fields and their approximations
Original languageEnglish
Pages (from-to)1449 - 1457
JournalInternational Journal of Bifurcation and Chaos
Volume13(6)
Publication statusPublished - Jun 2003

Bibliographical note

Publisher: World Scientific Publ Co Pte Ltd
Other identifier: IDS number 705DP

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