We study periodic orbits of the Reeb vector field on a nondegenerate dynamically convex starshaped hypersurface in along the lines of Long and Zhu [24], but using properties of the - equivariant symplectic homology. We prove that there exist at least distinct simple periodic orbits on any nondegenerate starshaped hypersurface in satisfying the condition that the minimal Conley–Zehnder index is at least . The condition is weaker than dynamical convexity.
Nous étudions les orbites périodiques du champ de Reeb sur les hypersurfaces non-dégénérées et dynamiquement convexes de en suivant les travaux de Long et Zhu mais en utilisant l’homologie symplectique -équivariante. Nous démontrons qu’il existe au moins orbites simples de Reeb sur toute hypersurface étoil�e et non dégénérée de satisfaisant la condition que le plus petit indice de Conley–Zehnder est au moins . Cette dernière condition est plus faible que celle de convexité dynamique.
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Keywords: Reeb dynamics, Equivariant symplectic homology, Index jump
@article{AIF_2016__66_6_2485_0,
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 = {https://aif.centre-mersenne.org/articles/10.5802/aif.3069/}
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Gutt, Jean; Kang, Jungsoo. On the minimal number of periodic orbits on some hypersurfaces in $\mathbb{R}^{2n}$. Annales de l'Institut Fourier, Volume 66 (2016) no. 6, pp. 2485-2505. doi : 10.5802/aif.3069. https://aif.centre-mersenne.org/articles/10.5802/aif.3069/
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