Classification of four-dimensional integrable Hamiltonian systems and Poisson actions of $\mathbb R^2$ in extended neighbourhoods of simple singular points. III.~Realization
Sbornik. Mathematics, Tome 186 (1995) no. 10, pp. 1477-1491
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The classification of integrable Hamiltonian systems in extended neighbourhoods of simple singular points, initiated in [1] and [2], is completed. This paper is a direct continuation
of [1] and [2] and uses all the concepts, definitions, and results presented there. As promised in [2], the aim here is to realize all admissible types of the invariants describing the iso-energetic equivalence of integrable Hamiltonian systems with two degrees of freedom in extended neighbourhoods of simple singular points. In doing that, all admissible types of Poisson actions of the group $\mathbb R^2$ on a four-dimensional symplectic manifold are also realized. Some of the examples constructed are of a purely illustrative nature, while others are more meaningful and occur in applications.
@article{SM_1995_186_10_a5,
author = {L. M. Lerman and Ya. L. Umanskii},
title = {Classification of four-dimensional integrable {Hamiltonian} systems and {Poisson} actions of $\mathbb R^2$ in extended neighbourhoods of simple singular points. {III.~Realization}},
journal = {Sbornik. Mathematics},
pages = {1477--1491},
publisher = {mathdoc},
volume = {186},
number = {10},
year = {1995},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1995_186_10_a5/}
}
TY - JOUR AU - L. M. Lerman AU - Ya. L. Umanskii TI - Classification of four-dimensional integrable Hamiltonian systems and Poisson actions of $\mathbb R^2$ in extended neighbourhoods of simple singular points. III.~Realization JO - Sbornik. Mathematics PY - 1995 SP - 1477 EP - 1491 VL - 186 IS - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_1995_186_10_a5/ LA - en ID - SM_1995_186_10_a5 ER -
%0 Journal Article %A L. M. Lerman %A Ya. L. Umanskii %T Classification of four-dimensional integrable Hamiltonian systems and Poisson actions of $\mathbb R^2$ in extended neighbourhoods of simple singular points. III.~Realization %J Sbornik. Mathematics %D 1995 %P 1477-1491 %V 186 %N 10 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_1995_186_10_a5/ %G en %F SM_1995_186_10_a5
L. M. Lerman; Ya. L. Umanskii. Classification of four-dimensional integrable Hamiltonian systems and Poisson actions of $\mathbb R^2$ in extended neighbourhoods of simple singular points. III.~Realization. Sbornik. Mathematics, Tome 186 (1995) no. 10, pp. 1477-1491. http://geodesic.mathdoc.fr/item/SM_1995_186_10_a5/