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00925njm 22002777a 4500 dc Calogero, F. author Gómez-Ullate Otaiza, David author Santin, Paolo M. author Sommacal, M author 2005-10-14 We introduce and discuss a simple Hamiltonian dynamical system, interpretable as a three-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. 0305-4470 10.1088/0305-4470/38/41/004 https://hdl.handle.net/20.500.14352/51453 http://dx.doi.org/10.1088/0305-4470/38/41/004 http://iopscience.iop.org http://arxiv.org/abs/nlin/0507024 The transition from regular to irregular motions, explained as travel on Riemann surfaces