Symmetrical Symplectic Capacity with Applications

Details Symmetrical Symplectic Capacity with Applications Symmetrical Symplectic Capacity with Applications

2010-11-24

arxiv.org/abs/1011.5291v1

Mathematics

Symplectic Geometry

28 pages, submitted

Scientific paper

In this paper, we first introduce the concept of symmetrical symplectic capacity for symmetrical symplectic manifolds, and by using this symmetrical symplectic capacity theory we prove that there exists at least one symmetric closed characteristic (brake orbit and $S$-invariant brake orbit are two examples) on prescribed symmetric energy surface which has a compact neighborhood with finite symmetrical symplectic capacity.

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