109 research outputs found
Floer homology for negative line bundles and Reeb chords in pre-quantization spaces
In this article we prove existence of Reeb orbits for Bohr-Sommerfeld
Legendrians in certain pre-quantization spaces. We give a quantitative estimate
from below. These estimates are obtained by studying Floer homology for
fibre-wise quadratic Hamiltonian functions on negative line bundles.Comment: 46 pages, 2 figures; v2: major revisio
Real holomorphic curves and invariant global surfaces of section
In this paper we prove that a dynamically convex starshaped hypersurface in
which is invariant under complex conjugation admits a global
surface of section which is invariant under conjugation as well. We obtain this
invariant global surface by embedding into and
applying a stretching argument to real holomorphic curves in .
The motivation for this result arises from recent progress in applying
holomorphic curve techniques to gain a deeper understanding on the dynamics of
the restricted three body problem.Comment: 36 page
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