We consider the Hamiltonian system (HS) ?J _ z = H z (t; z) where H 2 C 2 (R R 2N ; R) is 2-periodic in all variables, so (HS) induces a Hamiltonian system on the torus T 2N. In addition we assume that H is even in the z-variable. This implies the existence of 2 2N trivial stationary solutions of (HS). We are interested in the existence of nontrivial… (More)
We consider the existence of bound states for the coupled elliptic system ∆u 1 − λ 1 u 1 + µ 1 u 3
Recent developments in transition state theory brought about by dynamical systems theory are extended to time-dependent systems such as laser-driven reactions. Using time-dependent normal form theory, the authors construct a reaction coordinate with regular dynamics inside the transition region. The conservation of the associated action enables one to… (More)
This paper introduces a framework for a highly constrained sports scheduling problem which is modeled from the requirements of various professional sports leagues. We define a sports scheduling problem, introduce the necessary terminology and detail the constraints of the problem. A set of artificial and real-world instances derived from the actual problems… (More)
The paper is concerned with the local and global bifurcation structure of positive solutions u, v ∈ H 1 0 (() of the system −u + u = µ 1 u 3 + βv 2 u in −v + v = µ 2 v 3 + βu 2 v in of nonlinear Schrödinger (or Gross-Pitaevskii) type equations in ⊂ R N , N ≤ 3. The system arises in nonlinear optics and in the Hartree–Fock theory for a double condensate.… (More)
The crossing of a transition state in a multidimensional reactive system is mediated by invariant geometric objects in phase space: An invariant hyper-sphere that represents the transition state itself and invariant hyper-cylinders that channel the system towards and away from the transition state. The existence of these structures can only be guaranteed if… (More)
We establish a hierarchical ordering of periodic orbits in a strongly coupled multidimensional Hamiltonian system. Phase space structures can be reconstructed quantitatively from the knowledge of periodic orbits alone. We illustrate our findings for the hydrogen atom in crossed electric and magnetic fields.