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Tr. Mosk. Mat. Obs., 2013, Volume 74, Issue 1, Pages 75–113 (Mi mmo541)  

This article is cited in 2 scientific papers (total in 2 papers)

Hills formula for $g$-periodic trajectories of Lagrangian systems

M. N. Davletshin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In this paper some results of a work by Bolotin and Treshchëv are generalized to the case of $g$-periodic trajectories of Lagrangian systems. Formulae connecting the characteristic polynomial of the monodromy matrix with the determinant of the Hessian of the action functional are obtained both for the discrete and continuous cases. Applications to the problem of stability of $g$-periodic trajectories are given. Hills formula can be used to study $g$-periodic orbits obtained by variational methods.

Key words and phrases: Lagrangian systems; stability of $g$-periodic trajectories.

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English version:
Transactions of the Moscow Mathematical Society, 2013, 74, 65–96

Bibliographic databases:

UDC: 517.933
MSC: 34D05, 37J25, 70H03
Received: 06.03.2013
Revised: 07.03.2013

Citation: M. N. Davletshin, “Hills formula for $g$-periodic trajectories of Lagrangian systems”, Tr. Mosk. Mat. Obs., 74, no. 1, MCCME, M., 2013, 75–113; Trans. Moscow Math. Soc., 74 (2013), 65–96

Citation in format AMSBIB
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\by M.~N.~Davletshin
\paper Hills formula for $g$-periodic trajectories of Lagrangian systems
\serial Tr. Mosk. Mat. Obs.
\yr 2013
\vol 74
\issue 1
\pages 75--113
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\transl
\jour Trans. Moscow Math. Soc.
\yr 2013
\vol 74
\pages 65--96
\crossref{https://doi.org/10.1090/S0077-1554-2014-00213-2}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84924960172}


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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. Hu X., Ou Yu., Wang P., “Trace Formula For Linear Hamiltonian Systems With Its Applications To Elliptic Lagrangian Solutions”, Arch. Ration. Mech. Anal., 216:1 (2015), 313–357  crossref  mathscinet  zmath  isi  elib  scopus
    2. X. Hu, P. Wang, “Eigenvalue problem of Sturm-Liouville systems with separated boundary conditions”, Math. Z., 283:1-2 (2016), 339–348  crossref  mathscinet  zmath  isi  elib  scopus
  • Trudy Moskovskogo Matematicheskogo Obshchestva
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