Date: December 1995. Available electronically from dg-ga/9601003. The work of all three authors was partially supported by the NSF. 1 However, we will usually allow our closed two-forms to be degenerate. A similar cobordism technique has been developed and used independently of us by Shaun Martin in his study of Hamiltonian group actions on symplectic manifolds [Mar]. We wish to thank him for a...

The Weak KAM theory was developed by Fathi in order to study the dynamics of convex Hamiltonian systems. It somehow makes a bridge between viscosity solutions of the Hamilton-Jacobi equation and Mather invariant sets of Hamiltonian systems, although this was fully understood only a posteriori. These theories converge under the hypothesis of convexity, and the richness of applications mostly com...

The COntractor REnormalization group (CORE) method, a new approach to solving Hamiltonian lattice systems, is presented. The method defines a systematic and nonperturbative means of implementing KadanoffWilson real-space renormalization group transformations using cluster expansion and contraction techniques. We illustrate the approach and demonstrate its effectiveness using scalar field theory...

Motivated by quantum simulation, we consider lattice Hamiltonians for Yang-Mills gauge theories with finite group, example a subgroup of compact Lie group. We show that the electric Hamiltonian admits an interpretation as certain natural, nonunique Laplacian operator on Abelian or non-Abelian group and derive some consequences from this fact. Independent chosen Hamiltonian, provide full explici...

Let (M,ω) be a closed symplectic manifold and Ham(M,ω) the group of Hamiltonian diffeomorphisms of (M,ω). Then the Seidel homomorphism is a map from the fundamental group of Ham(M,ω) to the quantum homology ring QH∗(M ; Λ). Using this homomorphism we give a sufficient condition for when a nontrivial loop ψ in Ham(M,ω) determines a nontrivial loop ψ × idN in Ham(M ×N, ω ⊕ η), where (N, η) is a c...

We derive a variational characterization of the exact discrete Hamiltonian, which is a Type II generating function for the exact flow of a Hamiltonian system, by considering a Legendre transformation of Jacobi’s solution of the Hamilton–Jacobi equation. This provides an exact correspondence between continuous and discrete Hamiltonian mechanics, which arise from the continuousand discrete-time H...

In this paper I construct, using off the shelf components, a compact symplectic manifold with a non-trivial Hamiltonian circle action that admits no Kaehler structure. The non-triviality of the action is guaranteed by the existence of an isolated fixed point. The motivation for this work comes from the program of classification of Hamiltonian group actions. The Audin-Ahara-Hattori-Karshon class...

We prove that every RAAG (Right Angled Artin Group) embeds in the group of Hamiltonian symplectomorphisms of every symplectic manifold.

We show that the coupled mode equations for the stationary propagation of upper–hybrid and magnetoacoustic waves in magnetized electron–ion plasmas with negative group dispersion can be exactly derived from the generalized Hénon–Heiles Hamiltonian. The parameter regimes for the integrable cases of the coupled mode equations have been explicitly obtained. For positive group dispersion of the upp...

The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show that the Schrödinger equation for a nonrelativistic spinless particle is a classical equation which is equivalent to Hamilton’s equations. Our discussion is quite general, and incorporates time-dependent systems. This gives us the opportunity of discussing the gro...