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Hamiltonian Dynamical Systems: Symbolical, Numerical and Graphical Study

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Abstract

Hamiltonian dynamical systems can be studied from a variety of viewpoints. Our intention in this paper is to show some examples of usage of two Maxima packages for symbolical and numerical analysis (pdynamics and poincare, respectively), along with the set of scripts for obtaining the code corresponding to graphical representations of Poincaré sections, including animation movies.

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Acknowledgements

The authors express their gratitude to Masataka Kaneko (Tōhō University) and Yasuyuki Nakamura (Nagoya Institute of Technology) for many fruitful discussions about the topics in this paper. Thanks are also due to Richard Fateman for developing rkfun.

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  1. Faculty of Sciences, Tōhō University, Funabasi, Chiba, Japan

    Setsuo Takato

  2. Faculty of Sciences, State University of San Luis Potosí, San Luis Potosí, SLP, México

    José A. Vallejo

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  1. Setsuo Takato
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  2. José A. Vallejo
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Correspondence to José A. Vallejo.

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Work partially supported by Grants KAKENHI 15K01037 (ST, Japan) and CONACyT CB-2012 179115 (JAV, México).

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Takato, S., Vallejo, J.A. Hamiltonian Dynamical Systems: Symbolical, Numerical and Graphical Study. Math.Comput.Sci. 13, 281–295 (2019). https://doi.org/10.1007/s11786-019-00396-6

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  • DOI: https://doi.org/10.1007/s11786-019-00396-6

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