On the minimal number of periodic orbits on some hypersurfaces in 2n
[Sur le nombre minimal d’orbites périodiques sur certaines hypersurfaces de 2n ]
Annales de l'Institut Fourier, Tome 66 (2016) no. 6, pp. 2485-2505.

Nous étudions les orbites périodiques du champ de Reeb sur les hypersurfaces non-dégénérées et dynamiquement convexes de 2n en suivant les travaux de Long et Zhu mais en utilisant l’homologie symplectique S 1 -équivariante. Nous démontrons qu’il existe au moins n orbites simples de Reeb sur toute hypersurface étoil�e et non dégénérée de 2n satisfaisant la condition que le plus petit indice de Conley–Zehnder est au moins n-1. Cette dernière condition est plus faible que celle de convexité dynamique.

We study periodic orbits of the Reeb vector field on a nondegenerate dynamically convex starshaped hypersurface in 2n along the lines of Long and Zhu [24], but using properties of the S 1 - equivariant symplectic homology. We prove that there exist at least n distinct simple periodic orbits on any nondegenerate starshaped hypersurface in 2n satisfying the condition that the minimal Conley–Zehnder index is at least n-1. The condition is weaker than dynamical convexity.

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DOI : https://doi.org/10.5802/aif.3069
Classification : 53D10,  37J55
Mots clés : Dynamique de Reeb, Homologie symplectique équivariante, Saut d’indice
     author = {Gutt, Jean and Kang, Jungsoo},
     title = {On the minimal number of periodic orbits on some hypersurfaces in $\mathbb{R}^{2n}$},
     journal = {Annales de l'Institut Fourier},
     pages = {2485--2505},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {66},
     number = {6},
     year = {2016},
     doi = {10.5802/aif.3069},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.3069/}
AU  - Gutt, Jean
AU  - Kang, Jungsoo
TI  - On the minimal number of periodic orbits on some hypersurfaces in $\mathbb{R}^{2n}$
JO  - Annales de l'Institut Fourier
PY  - 2016
DA  - 2016///
SP  - 2485
EP  - 2505
VL  - 66
IS  - 6
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.3069/
UR  - https://doi.org/10.5802/aif.3069
DO  - 10.5802/aif.3069
LA  - en
ID  - AIF_2016__66_6_2485_0
ER  - 
Gutt, Jean; Kang, Jungsoo. On the minimal number of periodic orbits on some hypersurfaces in $\mathbb{R}^{2n}$. Annales de l'Institut Fourier, Tome 66 (2016) no. 6, pp. 2485-2505. doi : 10.5802/aif.3069. http://www.numdam.org/articles/10.5802/aif.3069/

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