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

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

2005-07-13

arxiv.org/abs/nlin/0507024v1

J. Phys. A 38 (2005), no. 41, 8873--8896

Nonlinear Sciences

Exactly Solvable and Integrable Systems

26 pages, 2 figures

Scientific paper

10.1088/0305-4470/38/41/004

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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