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.

For a preprint of the paper corresponding to this talk please see here (J. Phys. A: Math. Gen, in press)