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Topological Classification of Some SD Hamiltonian Systems

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Abstract

In this paper we classify the phase portraits in the Poincaré disk of the Smooth and Discontinuous (SD) Hamiltonian system with the rational Hamiltonian function \(H(x,y)=y^2/2+P(x)/Q(x,y)\), where \(P(x)=a\), ax, \(ax^2\) and \(Q(x,y)=Ax^2+By^2+C\).

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Acknowledgements

The first author is partially supported by National Natural Science Foundation of China (no. 12001112), Young Innovative Talents Program in Colleges and Universities of Guangdong Province (no.2019KQNCX211) and Science and Technology Program of Guangzhou (no. 202102020443). The third author is partially supported by the Agencia Estatal de Investigación Grant PID2019-104658GB-I00, and the H2020 European Research Council Grant MSCA-RISE-2017-777911.

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  1. School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou, 510320, People’s Republic of China

    Ting Chen

  2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, 08193, Barcelona, Catalonia, Spain

    Jaume Llibre

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  1. Ting Chen
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  2. Jaume Llibre
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Correspondence to Ting Chen.

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Chen, T., Llibre, J. Topological Classification of Some SD Hamiltonian Systems. Differ Equ Dyn Syst (2023). https://doi.org/10.1007/s12591-023-00637-y

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