Geometry of integrable dynamical systems on 2-dimensional surfaces

Details Geometry of integrable dynamical systems on 2-dimensional surfaces Geometry of integrable dynamical systems on 2-dimensional surfaces

2012-04-07

arxiv.org/abs/1204.1639v1

Mathematics

Dynamical Systems

31 pages, 12 figures, submitted to a special issue of Acta Mathematica Vietnamica

Scientific paper

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.

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