Relationship between singularities in classical mechanics for complex initial conditions and for complex time

T. Shnerb, K. G. Kay

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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 languageEnglish
Pages (from-to)165-173
Number of pages9
JournalNonlinear Dynamics
Volume42
Issue number2
DOIs
StatePublished - 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).

Keywords

  • Complex trajectories
  • Dynamical singularities
  • Integrability
  • Painlevé analysis
  • Semiclassical tunneling

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