Applications of Hofer's geometry to Hamiltonian dynamics
Author(s)
Date issued
2006
In
Commentarii Mathematici Helvetici
Vol
1
No
81
From page
105
To page
121
Subjects
Hofer-Zehnder capacity displacement energy Weinstein conjecture periodic orbits PSEUDO-HOLOMORPHIC-CURVES WEINSTEIN CONJECTURE PERIODIC-ORBITS ZEHNDER CAPACITY CRITICAL-VALUES FLOER HOMOLOGY MANIFOLDS ENERGY FLOWS SUBMANIFOLDS
Abstract
We prove that for every subset A of a tame symplectic manifold (W, omega) meeting a semi-positivity condition, the pi(1)-sensitive Hofer-Zehnder capacity of A is not greater than four times the stable displacement energy of A, c degrees(HZ) (A, W) = 0, of Hamiltonian diffeomorphisms generated by a compactly supported time-independent Hamiltonian stops to be a minimal geodesic in its homotopy class, then a non-constant contractible periodic orbit must appear.
Publication type
journal article
File(s)