Geodesic
Finite energy foliations of tight three-spheres and Hamiltonian dynamics
Helmut Hofer ; Kris Wysocki ; Eduard Zehnder1
1 Departement Mathematik, ETH-Zürich, 8092 Zürich, Switzerland
Annals of mathematics, Tome 157 (2003) no. 1, pp. 125-255.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Surfaces of sections are a classical tool in the study of $3$-dimensional dynamical systems. Their use goes back to the work of Poincaré and Birkhoff. In the present paper we give a natural generalization of this concept by constructing a system of transversal sections in the complement of finitely many distinguished periodic solutions. Such a system is established for nondegenerate Reeb flows on the tight $3$-sphere by means of pseudoholomorphic curves. The applications cover the nondegenerate geodesic flows on $T_1S^2\equiv \mathbb{R}P^3$ via its double covering $S^3$, and also nondegenerate Hamiltonian systems in $\mathbb{R}^4$ restricted to sphere-like energy surfaces of contact type.
DOI : 10.4007/annals.2003.157.125

Helmut Hofer  ; Kris Wysocki  ; Eduard Zehnder 1

1 Departement Mathematik, ETH-Zürich, 8092 Zürich, Switzerland 
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Helmut Hofer; Kris Wysocki; Eduard Zehnder. Finite energy foliations of tight three-spheres and Hamiltonian dynamics. Annals of mathematics, Tome 157 (2003) no. 1, pp. 125-255. doi : 10.4007/annals.2003.157.125. http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.125/

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