RT Journal Article
T1 Understanding complex dynamics by means of an associated Riemann surface
A1 Gómez-Ullate Otaiza, David
A1 Santini, M. P.
A1 Sommacal, M.
A1 Calogero, F.
AB We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the orbits can be derived, which is shown to depend on the initial data and the continued fraction expansion of a simple ratio of the coupling constants of the problem. For rational values of this ratio and generic values of the initial data, all orbits are periodic and the system is isochronous. For irrational values of the ratio, there exist periodic and quasi-periodic orbits for different initial data. Moreover, the dependence of the period on the initial data shows a rich behavior and initial data can always be found with arbitrarily large periods.
PB Elsevier
SN 0167-2789
YR 2012
FD 2012-08-15
LK https://hdl.handle.net/20.500.14352/44629
UL https://hdl.handle.net/20.500.14352/44629
LA eng
NO © 2012 Elsevier B.V. All rights reserved.It is a pleasure to acknowledge illuminating discussions with Carl Bender, Boris Dubrovin, Yuri Fedorov, Jean-Pierre Fran¸coise, Peter Grinevich and Fran¸cois  eyvraz. The research of DGU was supported in part by MICINN-FEDER grant MTM2009-06973 and CUR-DIUE grant 2009SGR859 and he would like to thank the financial support received from the Universita di Roma “La Sapienza” under the Accordo Bilaterale with Universidad Complutense de Madrid.
NO MICINN-FEDER
NO CUR-DIUE
NO Universita di Roma “La Sapienza”
DS Docta Complutense
RD 5 abr 2025