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Transactions of the Moscow Mathematical Society

ISSN 1547-738X(online) ISSN 0077-1554(print)

   
 
 

 

Hill's formula for $ g$-periodic trajectories of Lagrangian systems


Author: M. N. Davletshin
Translated by: E. Khukhro
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 74 (2013), vypusk 1.
Journal: Trans. Moscow Math. Soc. 2013, 65-96
MSC (2010): Primary 34D05; Secondary 37J25, 70H03
DOI: https://doi.org/10.1090/S0077-1554-2014-00213-2
Published electronically: April 9, 2014
MathSciNet review: 3235790
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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. Hill's formula can be used to study $ g$-periodic orbits obtained by variational methods.


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Additional Information

M. N. Davletshin
Affiliation: Moscow State University
Email: marsdavletshin@mail.ru

DOI: https://doi.org/10.1090/S0077-1554-2014-00213-2
Keywords: Lagrangian systems, stability of \boldmath$g$-periodic trajectories
Published electronically: April 9, 2014
Article copyright: © Copyright 2014 M. N. Davletshin

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