Applications of Hofer's geometry to Hamiltonian dynamics - Schlenk, Félix (My University, 2006)
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.
Keywords: 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