The first version of this paper is now finished. Here is the PDF file.
NT Zung & NV Minh, Geometry of integrable systems on 2D surfaces
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 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.
MSC: 58K50, 37J35, 58K45, 37J15
1st version, 06/Apr/2012, 31 pages, submitted to a special issue of Acta Mathematica Vietnamica
The paper is serious and could be sent to any rank-A journal instead of AMV which is a no-name journal. But we are sending it to AMV, because we promised to help AMV with a special issue which will contain good quality contributions from international mathematicians.