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This note corrects some typos and some errors in Introduction to Symplectic Topology (2nd edition, OUP 1998). In particular, in the latter book the statements of Theorem 6.36 (about Hamiltonian bundles) and Exercise 10.28 (about the structure of the group of symplectomorphisms of an open Riemann surface) need some modification. We thank everyone who pointed(More)
In this paper we prove Morse type inequalities for the contractible 1-periodic solutions of time dependent Hamiltonian differential equations on those compact symplectic manifolds M for which the symplectic form and the first Chern class of the tangent bundle vanish over q (M). The proof is based on a version of infinite dimensional Morse theory which is(More)
The object of this paper is to develop a unifying framework for the functional analytic representation of infinite dimensional linear systems with unbounded input and output operators. On the basis of the general approach new results are derived on the wellposedness of feedback systems and on the linear quadratic control problem. The implications of the(More)
Maslov's famous index for a loop of Lagrangian subspaces was interpreted by Arnold [1] as an intersection number with an algebraic variety known as the Maslov cycle. Arnold's general position arguments apply equally well to the case of a path of Lagrangian subspaces whose endpoints lie in the complement of the Maslov cycle. Our aim in this paper is to(More)
In this paper we define invariants of Hamiltonian group actions for central regular values of the moment map. The key hypotheses are that the moment map is proper and that the ambient manifold is symplectically aspherical. The invariants are based on the symplectic vortex equations. Applications include an existence theorem for relative periodic orbits, a(More)