English

On a Theorem by Ekeland-Hofer

Symplectic Geometry 2012-08-13 v2 Dynamical Systems

Abstract

In [EH89, Theorem 1] Ekeland-Hofer prove that for a centrally symmetric, restricted contact type hypersurface in R^{2n} and for any global, centrally symmetric Hamiltonian perturbation there exists a leaf-wise intersection point. In this note we show that if we replace restricted contact type by star-shaped there exists infinitely many leaf-wise intersection points or a leaf-wise intersection point on a closed characteristic.

Keywords

Cite

@article{arxiv.1001.3386,
  title  = {On a Theorem by Ekeland-Hofer},
  author = {Peter Albers and Urs Frauenfelder},
  journal= {arXiv preprint arXiv:1001.3386},
  year   = {2012}
}

Comments

5 pages, 1 figure; v2: minor changes

R2 v1 2026-06-21T14:36:46.087Z