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



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Calogero, F. and Gómez-Ullate Otaiza, David and Santin, Paolo M. and Sommacal, M (2005) The transition from regular to irregular motions, explained as travel on Riemann surfaces. Journal of physics A: Mathematical and general, 38 (41). pp. 8873-8896. ISSN 0305-4470

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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.

Item Type:Article
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© 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.

Uncontrolled Keywords:Many-body problem; Solvable dynamical-systems; Periodic-solutions; Differential-equations; Hamiltonian-systems; Oscillators; Painleve; Nonintegrability; Integrability; Galore
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:30881
Deposited On:15 Jun 2015 10:17
Last Modified:10 Dec 2018 15:09

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