Investigating non-integrability and chaos in complex time

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17 Citations (Scopus)

Abstract

The question of integrability of systems of ordinary differential equations (ODEs) has been studied extensively for centuries. Recently, however, owing to an upsurge of interest in chaos, a lot of studies have focused on the investigation of non-integrable systems, where chaos often manifests itself as "extremely sensitive dependence on initial conditions" of a dense set of real solutions in real time. Here, we argue that non-integrability can be efficiently investigated by solving ODEs in complex time and review recent results which strongly suggest that for a system of ODEs to be non-integrable it is necessary that it possess a dense set of infinitely-sheeted solutions in the complex domain.

Original languageEnglish
Pages (from-to)256-267
Number of pages12
JournalPhysica D: Nonlinear Phenomena
Volume86
Issue number1-2
DOIs
Publication statusPublished - Sep 1 1995

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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