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On Isochronicity

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Abstract

We obtain a complete set of explicit necessary and sufficient conditions for the isochronicity of a Hamiltonian system with one degree of freedom. The conditions are presented in terms of the Taylor coefficients of the Hamiltonian function and have the form of an infinite collection of polynomial equations.

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References

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Funding

This work was supported by the Russian Science Foundation under grant no. 20-11-20141, https://rscf.ru/project/20-11-20141/.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    D. V. Treschev

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  1. D. V. Treschev
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Correspondence to D. V. Treschev.

Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Vol. 322, pp. 206–232 https://doi.org/10.4213/tm4335.

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Treschev, D.V. On Isochronicity. Proc. Steklov Inst. Math. 322, 198–223 (2023). https://doi.org/10.1134/S008154382304017X

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  • DOI: https://doi.org/10.1134/S008154382304017X

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