2026-06-08T03:26:13Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/514532023-08-05T23:30:35Zcom_20.500.14352_14col_20.500.14352_15
The transition from regular to irregular motions, explained as travel on Riemann surfaces
Calogero, F.
Gómez-Ullate Otaiza, David
Santin, Paolo M.
Sommacal, M
51-73
Many-body problem
Solvable dynamical-systems
Periodic-solutions
Differential-equations
Hamiltonian-systems
Oscillators
Painleve
Nonintegrability
Integrability
Galore
Física-Modelos matemáticos
Física matemática
© 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
2023-06-20T10:55:17Z
2023-06-20T10:55:17Z
2005-10-14
journal article
https://hdl.handle.net/20.500.14352/51453
0305-4470
10.1088/0305-4470/38/41/004
eng
open access
application/pdf
IOP Publishing