The Weinstein conjecture and the theorems of nearby and almost existence

Details The Weinstein conjecture and the theorems of nearby and almost existence The Weinstein conjecture and the theorems of nearby and almost existence

2003-10-21

arxiv.org/abs/math/0310330v2

Mathematics

Differential Geometry

29 pages; revised version: minor changes, references added, Proposition 4.4 corrected

Scientific paper

The Weinstein conjecture, as the general existence problem for periodic orbits of Hamiltonian or Reeb flows, has been among the central questions in symplectic topology for over two decades and its investigation has led to understanding of some fundamental properties of Hamiltonian flows. In this paper we survey some recently developed and well-known methods of proving various particular cases of this conjecture and the closely related almost existence theorem. We also examine differentiability and continuity properties of the Hofer-Zehnder capacity function and relate these properties to the features of the underlying Hamiltonian dynamics, e.g., to the period growth.

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