Acta Mathematica Vietnamica
- Volume 49
- Volume 48
- Volume 47
- Volume 46
- Volume 45
- Volume 44
- Volume 43
- Volume 42
- Volume 41
- Volume 40
- Volume 39
- Volume 38
- Volume 37
- Volume 36
- Volume 35
- Volume 34
- Volume 33
- Volume 32
- Volume 31
- Volume 30
- Volume 29
- Volume 28
- Volume 27
- Volume 26
- Volume 25
- Volume 24
- Volume 23
- Volume 22
- Volume 21
- Volume 20
- Volume 19
- Volume 18
- Volume 17
- Volume 16
- Volume 15
- Volume 14
- Volume 13
- Volume 12
- Volume 11
- Volume 10
- Volume 9
- Volume 8
- Volume 7
- Volume 6
- Volume 5
- Volume 4
- Volume 3
- Volume 2
- Volume 1
Geometry of integrable dynamical systems on 2-dimensional surfaces
Nguyen Tien Zung
,
Nguyen Van Minh
Abstract
This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous invariants involved in this classification are the left equivalence classes of period or monodromy functions and the cohomology classes of period cocycles, which can be expressed in terms of Puiseux series. We also study the problem of Hamiltonianization of these integrable vector fields by a compatible symplectic or Poisson structure.