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 |
|---|---|
| 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 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Condensed Matter Physics
- Statistical and Nonlinear Physics
Cite this
Investigating non-integrability and chaos in complex time. / Bountis, Tassos.
In: Physica D: Nonlinear Phenomena, Vol. 86, No. 1-2, 01.09.1995, p. 256-267.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Investigating non-integrability and chaos in complex time
AU - Bountis, Tassos
PY - 1995/9/1
Y1 - 1995/9/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0039577818&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0039577818&partnerID=8YFLogxK
U2 - 10.1016/0167-2789(95)00106-E
DO - 10.1016/0167-2789(95)00106-E
M3 - Article
AN - SCOPUS:0039577818
VL - 86
SP - 256
EP - 267
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 1-2
ER -