# zbMATH — the first resource for mathematics

Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity. (Russian) Zbl 0696.58019
One can imagine the main purpose of this work from the following complete table of contents (nice figures and tablets are included as well):
§1. Introduction
1.1 Hamiltonian systems
1.2 The Bott integrals
1.3 Behaviour of the Liouville tori
1.4 Topological equivalence of integrable Hamiltonian systems
1.5 Formulation of problems
1.6 Scelets and complexity of integrable Hamiltonian systems
1.7 Tablet of integrable Hamiltonian systems of a small complexity
1.8 Real physical systems and their position in the tablet of complexity
§2. Theorems of realization
2.1 Letters-atoms and their Seifert realization
2.2 Seifert’s decomposition of a three-dimensional manifold
2.3 Proof of the theorem of realization
2.4 Identification of abstract and geometric scelets
§3. Equipped scelets
3.2 Superfluously equipped scelets
3.3 Equipped scelets
3.4 Influence of orientation
§4. Codation of integrable Hamiltonian systems
4.1 Representation of letters-atoms
4.2 Words-molecules
4.3 Indicated words-molecules
4.4 Physical systems.
Reviewer: J.Andres

##### MSC:
 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.) 54H20 Topological dynamics (MSC2010) 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
##### Keywords:
classification; integrable Hamiltonian systems