A TOPOLOGICAL INVARIANT AND A CRITERION FOR THE EQUIVALENCE OF INTEGRABLE HAMILTONIAN-SYSTEMS WITH 2 DEGREES OF FREEDOM

被引：0

作者：

FOMENKO, AT

SISHANG, KT

机构：

来源：

MATHEMATICS OF THE USSR-IZVESTIYA | 1990年 / 54卷 / 03期

关键词：

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A new topological invariant is constructed which classifies integrable Hamiltonian systems with two degrees of freedom (admitting a Bott integral). A criterion for the equivalence of Bott systems is proved: such systems are topologically equivalent if and only if their topological invariants coincide. The topological invariant is effectively calculated for specific integrable Hamiltonian systems in physics and mechanics.

引用

页码：567 / 596

页数：30

共 50 条

[1] TOPOLOGICAL CLASSIFICATION OF INTEGRABLE HAMILTONIAN-SYSTEMS WITH 2 DEGREES OF FREEDOM - LIST OF SYSTEMS OF SMALL COMPLEXITY
BOLSINOV, AV
MATVEEV, SV
FOMENKO, AT
[J]. RUSSIAN MATHEMATICAL SURVEYS, 1990, 45 (02) : 59 - 94
[2] A BORDISM THEORY FOR INTEGRABLE NONDEGENERATE HAMILTONIAN-SYSTEMS WITH 2-DEGREES OF FREEDOM - A NEW TOPOLOGICAL INVARIANT OF HIGHER-DIMENSIONAL INTEGRABLE SYSTEMS
FOMENKO, AT
[J]. MATHEMATICS OF THE USSR-IZVESTIYA, 1992, 39 (01): : 731 - 759
[3] ORBITAL EQUIVALENCE OF INTEGRABLE HAMILTONIAN-SYSTEMS WITH 2 DEGREES OF FREEDOM - A CLASSIFICATION THEOREM .1.
BOLSINOV, AV
FOMENKO, AT
[J]. RUSSIAN ACADEMY OF SCIENCES SBORNIK MATHEMATICS, 1995, 81 (02) : 421 - 465
[4] A SMOOTH TRAJECTORY CLASSIFICATION OF INTEGRABLE HAMILTONIAN-SYSTEMS WITH 2 DEGREES OF FREEDOM
BOLSINOV, AV
[J]. SBORNIK MATHEMATICS, 1995, 186 (1-2) : 1 - 27
[5] LAGRANGIAN PROJECTIONS OF INVARIANT TORI OF HAMILTONIAN-SYSTEMS WITH 2 DEGREES OF FREEDOM
BYALYI, ML
POLTEROVICH, LV
[J]. FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 1989, 23 (01) : 54 - 55
[6] LAGRANGIAN SINGULARITIES OF INVARIANT TORI OF HAMILTONIAN-SYSTEMS WITH 2 DEGREES OF FREEDOM
BIALY, ML
POLTEROVICH, LV
[J]. INVENTIONES MATHEMATICAE, 1989, 97 (02) : 291 - 303
[7] ON THE NUMBER OF CAUSTICS FOR INVARIANT TORI OF HAMILTONIAN-SYSTEMS WITH 2 DEGREES OF FREEDOM
BIALY, M
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1991, 11 : 273 - 278
[8] SMOOTH TRAJECTORY CLASSIFICATION OF INTEGRABLE HAMILTONIAN-SYSTEMS WITH 2 DEGREES OF FREEDOM - THE CASE OF SYSTEMS WITH PLANAR ATOMS
BOLSINOV, AV
[J]. RUSSIAN MATHEMATICAL SURVEYS, 1994, 49 (03) : 181 - 182
[9] HORSESHOES IN PERTURBATIONS OF HAMILTONIAN-SYSTEMS WITH 2 DEGREES OF FREEDOM
HOLMES, PJ
MARSDEN, JE
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1982, 82 (04) : 523 - 544
[10] EXPANSIVITY FOR OPTICAL HAMILTONIAN-SYSTEMS WITH 2 DEGREES OF FREEDOM
PATERNAIN, GP
PATERNAIN, M
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1993, 316 (08): : 837 - 841

← 1 2 3 4 5 →