Relationship Between Singularities in Classical Mechanics for Complex Initial Conditions and for Complex Time |
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| Authors: | T Shnerb K G Kay |
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| Institution: | (1) Department of Chemistry, Bar-Ilan University, Ramat-Gan, 52900, Israel |
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| 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. |
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| Keywords: | complex trajectories dynamical singularities integrability Painlevé analysis semiclassical tunneling |
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