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Phenomena of nonintegrability in Hamiltonian systems. (English) Zbl 0675.58015

Proc. Int. Congr. Math., Berkeley/Calif. 1986, Vol. 2, 1161-1170 (1987).
[For the entire collection see Zbl 0657.00005.]
The author discusses the notions of the integrability and the nonintegrability of a dynamical system and gives a survey of results connected with the nonintegrability. The existence and the non-existence of smooth and analytic integrals, the integrals of perturbed systems, the topological obstructions to the existence of analytic integrals etc. are among the main topics of the paper.
Reviewer: Yu.E.Gliklikh

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
70H05 Hamilton’s equations

Citations:

Zbl 0657.00005