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Buslaev, V. S.; Nalimova, E. A.

Trace formula in general Hamiltonian mechanics. (English. Russian original) Zbl 0598.70018

Theor. Math. Phys. 60, 863-871 (1984); translation from Teor. Mat. Fiz. 60, No. 3, 344-355 (1984).
This paper studies theoretically the variational equation corresponding to a fixed trajectory interval which generates a linear differential operator. A trace formula is considered which connects this operator with the Jacobian of certain transformations. The authors are primarily interested in the influence of geometrical structures on the trace formula. No physical or technical applications of the developed formalism are given.
Reviewer: N.Arley

Cited in 1 Document

MSC:

70H05 Hamilton’s equations
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems

Keywords:

Jacobi operator; variational equation; fixed trajectory interval; trace formula; Jacobian of certain transformations
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\textit{V. S. Buslaev} and \textit{E. A. Nalimova}, Theor. Math. Phys. 60, 863--871 (1984; Zbl 0598.70018); translation from Teor. Mat. Fiz. 60, No. 3, 344--355 (1984)
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References:

[1] M. Kac, Integration in Function Spaces and Some of Its Applications, Pisa (1980). · Zbl 0504.28015
[2] V. S. Buslaev, Dokl. Akad. Nauk SSSR,182, 743 (1968).
[3] A. N. Vasil’ev, Functional Methods in Quantum Field Theory and Statistics [in Russian], State University, Leningrad (1976).
[4] V. S. Buslaev and E. A. Rybakina, ?Trace formula in Hamiltonian mechanics,? Zap. Nauchn. Semin. LOMI,115, 40 (1982). · Zbl 0537.70016
[5] F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, and D. Sternheimer, Ann. Phys. (N.Y.),111, 61 (1978). · Zbl 0377.53024
[6] I. Ts. Gokhberg and M. G. Krein, Theory of Volterra Operators in Hilbert Space and Its Applications [in Russian], Nauka, Moscow (1967). · Zbl 0161.11601
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.