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Noncanonical time transformations relating finite-dimensional integrable systems

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Abstract

We consider dual Stäckel schemes related to each other by a noncanonical transformation of the time variable. We prove that this duality of different integrable systems arises from the multivaluedness of the Abel mapping. We construct the Lax matrices and the r-matrix algebras for some integrable systems on a plane. The integrable deformations of the Kepler problem and the Holt-type systems are considered in detail.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    A. V. Tsyganov

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  1. A. V. Tsyganov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 120, No. 1, pp. 27–53, July 1999.

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Tsyganov, A.V. Noncanonical time transformations relating finite-dimensional integrable systems. Theor Math Phys 120, 840–861 (1999). https://doi.org/10.1007/BF02557394

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  • DOI: https://doi.org/10.1007/BF02557394

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