## 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

### Keywords:

integrability; nonintegrability; dynamical system

Zbl 0657.00005