Round Morse functions and isoenergy surfaces of integrable Hamiltonian systems
Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 319-336
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A study is made of the topology of a class of three-dimensional manifolds that arise as constant energy surfaces for integrable systems. It is proved that this class coincides with the class of manifolds admitting a function all of whose critical manifolds are nondegenerate circles and whose nonsingular level surfaces are disjoint unions of tori. Necessary and sufficient conditions are obtained for the existence of minimal round Morse functions on manifolds of dimension greater than five.
Figures: 3.
Bibliography: 20 titles.
@article{SM_1989_63_2_a3,
author = {S. V. Matveev and A. T. Fomenko and V. V. Sharko},
title = {Round {Morse} functions and isoenergy surfaces of integrable {Hamiltonian} systems},
journal = {Sbornik. Mathematics},
pages = {319--336},
publisher = {mathdoc},
volume = {63},
number = {2},
year = {1989},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1989_63_2_a3/}
}
TY - JOUR AU - S. V. Matveev AU - A. T. Fomenko AU - V. V. Sharko TI - Round Morse functions and isoenergy surfaces of integrable Hamiltonian systems JO - Sbornik. Mathematics PY - 1989 SP - 319 EP - 336 VL - 63 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_1989_63_2_a3/ LA - en ID - SM_1989_63_2_a3 ER -
S. V. Matveev; A. T. Fomenko; V. V. Sharko. Round Morse functions and isoenergy surfaces of integrable Hamiltonian systems. Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 319-336. http://geodesic.mathdoc.fr/item/SM_1989_63_2_a3/