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TMF, 1999, Volume 120, Number 1, Pages 27–53 (Mi tmf758)  

This article is cited in 3 scientific papers (total in 3 papers)

Noncanonical time transformations relating finite-dimensional integrable systems

A. V. Tsiganov

St. Petersburg State University, Faculty of Physics

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.

DOI: https://doi.org/10.4213/tmf758

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English version:
Theoretical and Mathematical Physics, 1999, 120:1, 840–861

Bibliographic databases:

Received: 11.11.1998

Citation: A. V. Tsiganov, “Noncanonical time transformations relating finite-dimensional integrable systems”, TMF, 120:1 (1999), 27–53; Theoret. and Math. Phys., 120:1 (1999), 840–861

Citation in format AMSBIB
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\paper Noncanonical time transformations relating finite-dimensional integrable systems
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\transl
\jour Theoret. and Math. Phys.
\yr 1999
\vol 120
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\pages 840--861
\crossref{https://doi.org/10.1007/BF02557394}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Tsiganov, “Canonical transformations of the extended phase space and integrable systems”, Theoret. and Math. Phys., 124:1 (2000), 918–937  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. V. Tsiganov, “Degenerate integrable systems on the plane with a cubic integral of motion”, Theoret. and Math. Phys., 124:3 (2000), 1217–1233  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. A. V. Tsiganov, “Construction of Separation Variables for Finite-Dimensional Integrable Systems”, Theoret. and Math. Phys., 128:2 (2001), 1007–1024  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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