Periodic Hamiltonian flows on four dimensional manifolds / Yael Karshon

Auteur principal : Karshon, Yael, 1964-, AuteurType de document : MonographieCollection : Memoirs of the American Mathematical Society, 672Langue : anglais.Pays: Etats Unis.Éditeur : Providence : American Mathematical Society, 1999Description : 1 vol. (VIII-71 p.) : fig. ; 26 cmISBN: 0821811819.ISSN: 0065-9266.Bibliographie : Bibliogr. p. 69-71.Sujet MSC : 70H12, Mechanics of particles and systems, Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics
70G45, Mechanics of particles and systems, Differential geometric methods for problems in mechanics
37N05, Applications of dynamical systems, Dynamical systems in classical and celestial mechanics
En-ligne : ArXiv
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A complete classification of Hamiltonian circle actions (that is, periodic Hamiltonian flows or Hamiltonian S 1 -spaces) on compact 4-dimensional manifolds is given: first studying how to characterize the isomorphic S 1 -spaces, and second, listing all these spaces and determining the kind of invariant symplectic forms with which the manifolds are endowed. In this way, this work completes some previous ones on the same subject: see e.g.: M. Audin [in Géométrie symplectique et mécanique, Colloq. Int. Sémin. Sud-Rhodan. Géom. V, La Grande Motte/Fr. 1988, Lect. Notes Math. 1416, 1-25 (1990; Zbl 0699.58031)], and K. Ahara and A. Hattori [J. Fac. Sci., Univ. Tokyo, Sect. IA 38, 251-298 (1991; Zbl 0749.53018)]. It is also proved that all these compact 4-dimensional Hamiltonian S 1 -spaces are Kähler manifolds, but this result does not hold for higher-order dimensional manifolds. (Zentralblatt)

Bibliogr. p. 69-71

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