Dufour, Jean-Paul; Molino, Pierre; Toulet, Anne Classification of integrable systems on two-dimensional manifolds and invariants in Fomenko’s models. (Classification des systèmes intégrables en dimension 2 et invariants des modèles de Fomenko.) (French) Zbl 0808.58025 C. R. Acad. Sci., Paris, Sér. I 318, No. 10, 949-952 (1994). The classification problem which the authors study here is related to triples of the type \((M, \omega, {\mathcal F})\) where \(M\) denotes an oriented compact connected 2-dimensional manifold, \(\omega\) is a symplectic form on \(M\) and \(\mathcal F\) is a Morse foliation on \(M\), that is a foliation with singularities having the property that for every leaf \(F\) of \(\mathcal F\) there exists a neighbourhood \(\mathcal U\), saturated by the foliation and a proper Morse function \(f_{\mathcal U}\) on \(\mathcal U\) such that the restriction \({\mathcal F}\mid_{\mathcal U}\) is defined by the level lines of \(f_{\mathcal U}\); the equivalences are the symplectomorphisms which preserve the foliations. So, some invariants are associated to the triple \((M, \omega, {\mathcal F})\), among these being the Taylor coefficients corresponding to bifurcation points. Such invariants can be found in Fomenko’s models for Liouville’s torus bifurcations. Reviewer: L.Maxim-Răileanu (Iaşi) Cited in 1 ReviewCited in 14 Documents MSC: 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 57R30 Foliations in differential topology; geometric theory Keywords:classification; Morse foliation; symplectomorphisms; invariants PDF BibTeX XML Cite \textit{J.-P. Dufour} et al., C. R. Acad. Sci., Paris, Sér. I 318, No. 10, 949--952 (1994; Zbl 0808.58025)