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Algebra and Geometry Through Hamiltonian Systems

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Continuous and Distributed Systems

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 211))

Abstract

Hamiltonian systems are considered to be the prime tool of classical and quantum mechanics. The proper investigation of such systems usually requires deep results from algebra and geometry. Here we present several results which in some sense go the opposite way: the knowledge about the integrable system enables us to obtain results on geometric and algebraic structures which naturally appear in such problems. All the results were obtained by employees of the Chair of Differential Geometry and Applications in Moscow State University in 2011–2012.

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Acknowledgments

This work was supported by the Government grant of the Russian Federation for support of research projects implemented by leading scientists, in the Federal State Budget Educational Institution of Higher Professional Education Lomonosov Moscow State University under the agreement No. 11.G34.31.0054.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, Russian Federation, 119991

    Anatoly T. Fomenko & Andrei Konyaev

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  1. Anatoly T. Fomenko
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  2. Andrei Konyaev
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Correspondence to Anatoly T. Fomenko .

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Editors and Affiliations

  1. National Academy of Science, National Technical University of Ukraine, Kiev, Ukraine

    Mikhail Z. Zgurovsky

  2. Lomonosov Moscow State University, Moscow, Russia

    Victor A. Sadovnichiy

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Fomenko, A.T., Konyaev, A. (2014). Algebra and Geometry Through Hamiltonian Systems. In: Zgurovsky, M., Sadovnichiy, V. (eds) Continuous and Distributed Systems. Solid Mechanics and Its Applications, vol 211. Springer, Cham. https://doi.org/10.1007/978-3-319-03146-0_1

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  • DOI: https://doi.org/10.1007/978-3-319-03146-0_1

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