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Existence of a capacity
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1-periodic action Alexander-Spanier cohomology Arnold conjecture Assume assumption Axiom boundary bounded sets bundle capacity function Chapter closed characteristic cohomology compact symplectic manifold complex structure conclude Consequently consider constant contact type convex coordinates critical points defined definition denote diffeomorphism diffeomorphism ip differential equations dimensional estimate exists finite fixed points Floer homology Fredholm function H geodesic geometric global gradient equation Hamiltonian equation Hamiltonian function Hamiltonian system Hamiltonian vector field hence Hofer holomorphic homeomorphism homotopy hypersurface integrable isomorphism Lemma linear map map ip monotonicity Moreover Morse nondegenerate open neighborhood open set periodic orbits periodic solutions proof of Theorem Proposition prove Recall regular energy surface Riemannian metric satisfying sequence smooth function subset subspace symplectic diffeomorphism symplectic embedding symplectic invariants symplectic manifold symplectic map symplectic structure theory topology torus vector field Xh verifies Xh(x