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The Transition from Regular to Irregular Motions, Explained as Travel on Riemann Surfaces

F. Calogero·D. Gomez-Ullate·P. M. Santini·M. Sommacal
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Abstract

We introduce and discuss a simple Hamiltonian dynamical system, interpretable as a 3-body problem in the complex plane and providing the prototype of a mechanism explaining the transition from regular to irregular motions as travel on Riemann surfaces. The interest of this phenomenology -- illustrating the onset in a deterministic context of irregular motions -- is underlined by its generality, suggesting its eventual relevance to understand natural phenomena and experimental investigations. Here only some of our main findings are reported, without detailing their proofs: a more complete presentation will be published elsewhere.

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F. Calogero, D. Gomez-Ullate, P. M. Santini, M. Sommacal. 2005-07-13. The Transition from Regular to Irregular Motions, Explained as Travel on Riemann Surfaces. https://doi.org/10.1088/0305-4470%2F38%2F41%2F004

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