The transition from regular to irregular motions, explained as travel on Riemann surfaces

© IOP Publishing. It is a pleasure to acknowledge illuminating discussions with Boris Dubrovin, Yuri Fedorov, Jean-Pierre Fran¸coise, Fran¸cois Leyvraz, Jaume Llibre, Alexander Mikhailov and Carles Simó.
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.
Depto. de Física Teórica
Fac. de Ciencias Físicas
TRUE
pub