Smooth normal forms for integrable Hamiltonian systems near a focus–focus singularity

Belitskii, G.R., Kopanskii, A.Ya.: Equivariant Sternberg–Chen theorem. J. Dyn. Differ. Equ. 14(2), 349–367 (2002)

Borel, E.: Mémoire sur les séries divergentes. Ann. Sci. Éc. Norm. Super. 16, 9–131 (1899)

Chaperon, M.: Quelques outils de la théorie des actions différentiables. In: IIIe rencontre de géométrie de Schnepfenried. Astérisque, vol. 107–108 (1982)

Chaperon, M.: Géométrie différentielle et singularités de systèmes dynamiques, No. 138–139. Société Mathématique de France, Paris (1986)

Chaperon, M.: Normalisation of the smooth focus–focus: a simple proof. With an appendix by Jiang Kai. Acta Math. Vietnam. (2013). doi: 10.1007/s40306-012-0003-y

Colin de Verdière, Y., Vey, J.: Le lemme de Morse isochore. Topology 18, 283–293 (1979)

Eliasson, L.H.: Hamiltonian systems with Poisson commuting integrals. Ph.D. thesis, University of Stockholm (1984)

Miranda, E., Vũ Ngọc, S.: A singular Poincaré lemma. Int. Math. Res. Not. 2005(1), 27–45 (2005)

Miranda, E., Zung, N.T.: Equivariant normal form for nondegenerate singular orbits of integrable Hamiltonian systems. Ann. Sci. Éc. Norm. Super. 37(6), 819–839 (2004)

Vey, J.: Sur certains systèmes dynamiques séparables. Am. J. Math. 100, 591–614 (1978)

Vũ Ngọc, S.: On semi-global invariants for focus–focus singularities. Topology 42(2), 365–380 (2003)

Williamson, J.: On the algebraic problem concerning the normal form of linear dynamical systems. Am. J. Math. 58(1), 141–163 (1936)

Zung, N.T.: Another note on focus–focus singularities. Lett. Math. Phys. 60, 87–99 (2003)

Zung, N.T.: Torus actions and integrable systems. In: Bolsinov, A.V., Fomenko, A.T., Oshmenko, A.A. (eds.) Topological Methods in the Theory of Integrable Systems, pp. 289–330. Cambridge Scientific Publishers, Cambridge (2006)