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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics