Abstract
A relationship is established between the functional forms of two kinds of singularities in dynamical variables that arise in complexified versions classical mechanics: singularities that are treated as a functions of complex initial conditions for real time and those that are treated as a functions of complex time for real initial conditions. The analysis is verified by numerical calculations. The results imply that Kowaleskaya-Painlevé condition for integrability can be phrased in terms of singularities with respect to initial conditions.
| Original language | English |
|---|---|
| Pages (from-to) | 165-173 |
| Number of pages | 9 |
| Journal | Nonlinear Dynamics |
| Volume | 42 |
| Issue number | 2 |
| DOIs | |
| State | Published - Oct 2005 |
Bibliographical note
Funding Information:Tamar Shnerb thanks Prof. E. J. Heller for helpful discussions on the subject of Painlevé singularities. This work was supported by the Israel Science Foundation (Grant No. 85/03).
Funding
Tamar Shnerb thanks Prof. E. J. Heller for helpful discussions on the subject of Painlevé singularities. This work was supported by the Israel Science Foundation (Grant No. 85/03).
| Funders | Funder number |
|---|---|
| Israel Science Foundation | 85/03 |
Keywords
- Complex trajectories
- Dynamical singularities
- Integrability
- Painlevé analysis
- Semiclassical tunneling