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 language | English |
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Pages (from-to) | 256-267 |
Number of pages | 12 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 86 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - Sep 1 1995 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics