Geometry, Spectral Theory, Groups, and Dynamics
Michael Entov, Yehuda Pinchover, Michah Sageev · Contemporary mathematics - American Mathematical Society · 2005
Ab s t r a c t .An action selector for a symplectic manifold (A/,cu) associates with each compactly supported Hamiltonian function H on M an action value of H in a suitable way.Action selectors are known to exist for a broad class of symplectic manifolds.We show how the existence of an action selector leads to sharp energy capacity inequalities between the Gromov width, the Hofer-Zehnder capacity, and the displacement energy.We also obtain sharp lower bounds for the smallest action of a closed characteristic on contact type hypersurfaces., J x Jo and its action spectrum is E°(H) = {A H ( ä ) |( a :,ä ) e P o (/f)}.Note that for a G S°(H ) the set a 4 -td(7r2(A/)) also belongs to As a consequence, S°(H ) need not be closed and is dense in R if a;(7r2(A/)) is dense.For 2000 Mathematics