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Numerical and Theoretical Studies on the Rational Standard
Map at Moderate-to-Large Values of the Amplitude Parameter
Pablo M. Cincottaa, Claudia M. Giordanoa, Carles Simób a Grupo de Caos en Sistemas Hamiltonianos, Facultad de Ciencias Astronómicas y Geofísicas,
Universidad Nacional de La Plata and Instituto de Astrofísica de La Plata (CONICET),
Paseo del Bosque S/N, B1900FWA La Plata, Argentina
b Departament de Matemàtiques i Informàtica, Universitat de Barcelona,
Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
Abstract:
In this work an exhaustive numerical and analytical investigation of the dynamics
of a bi-parametric symplectic map, the so-called rational standard map, at moderate-to-large
values of the amplitude parameter is addressed. After reviewing the model, a discussion
concerning an analytical determination of the maximum Lyapunov exponent is provided
together with thorough numerical experiments. The theoretical results are obtained in the
limit of a nearly uniform distribution of the phase values. Correlations among phases lead to
departures from the expected estimates. In this direction, a detailed study of the role of stable
periodic islands of periods 1, 2 and 4 is included. Finally, an experimental relationship between
the Lyapunov and instability times is shown, while an analytical one applies when correlations
are irrelevant, which is the case, in general, for large values of the amplitude parameter.
Keywords:
analytical and numerical methods, periodic orbits, chaos, area-preserving maps.
Received: 24.01.2023 Accepted: 26.04.2023
Citation:
Pablo M. Cincotta, Claudia M. Giordano, Carles Simó, “Numerical and Theoretical Studies on the Rational Standard
Map at Moderate-to-Large Values of the Amplitude Parameter”, Regul. Chaotic Dyn., 28:3 (2023), 265–294
Linking options:
https://www.mathnet.ru/eng/rcd1205 https://www.mathnet.ru/eng/rcd/v28/i3/p265
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Abstract page: | 62 | References: | 16 |
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