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TMF, 1984, Volume 61, Number 1, Pages 52–63 (Mi tmf5657)  

This article is cited in 1 scientific paper (total in 2 paper)

Trace formula in Lagrangian mechanics

V. S. Buslaev, E. A. Nalimova


Abstract: The variational equation (Jacobi equation) on a fixed trajectory of a natural Lagrangian system leads to a certain linear differential operator. The trace formula expresses a suitably regularized determinant of this operator in terms of the determinant of a finite-dimensional operator generated by the classical motion in the neighborhood of the trajectory. The aim of the paper is to discuss such a formula in a fairly free geometrical framework and establish its connection with the trace formula in general Hamiltonian mechanics, which was the subject of a preceding publication of the authors.

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English version:
Theoretical and Mathematical Physics, 1984, 61:1, 989–997

Bibliographic databases:

Received: 14.10.1983

Citation: V. S. Buslaev, E. A. Nalimova, “Trace formula in Lagrangian mechanics”, TMF, 61:1 (1984), 52–63; Theoret. and Math. Phys., 61:1 (1984), 989–997

Citation in format AMSBIB
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\by V.~S.~Buslaev, E.~A.~Nalimova
\paper Trace formula in Lagrangian mechanics
\jour TMF
\yr 1984
\vol 61
\issue 1
\pages 52--63
\mathnet{http://mi.mathnet.ru/tmf5657}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=774207}
\zmath{https://zbmath.org/?q=an:0598.70023}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 61
\issue 1
\pages 989--997
\crossref{https://doi.org/10.1007/BF01038547}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984AGK6100006}


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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. V. V. Trofimov, M. V. Shamolin, “Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems”, J. Math. Sci., 180:4 (2012), 365–530  mathnet  crossref  mathscinet
    2. V. M. Babich, A. M. Budylin, L. A. Dmitrieva, A. I. Komech, S. B. Levin, M. V. Perel', E. A. Rybakina, V. V. Sukhanov, A. A. Fedotov, “On the mathematical work of Vladimir Savel'evich Buslaev”, St. Petersburg Math. J., 25:2 (2014), 151–174  mathnet  crossref  mathscinet  zmath  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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