location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword Hamiltonian

 Expand all        Collapse all Results 1 - 5 of 5

1. CJM Online first

Santoprete, Manuele; Scheurle, Jürgen; Walcher, Sebastian
 Motion in a Symmetric Potential on the Hyperbolic Plane We study the motion of a particle in the hyperbolic plane (embedded in Minkowski space), under the action of a potential that depends only on one variable. This problem is the analogous to the spherical pendulum in a unidirectional force field. However, for the discussion of the hyperbolic plane one has to distinguish three inequivalent cases, depending on the direction of the force field. Symmetry reduction, with respect to groups that are not necessarily compact or even reductive, is carried out by way of Poisson varieties and Hilbert maps. For each case the dynamics is discussed, with special attention to linear potentials. Keywords:Hamiltonian systems with symmetry, symmetries, non-compact symmetry groups, singular reductionCategories:37J15, 70H33, 70F99, 37C80, 34C14, , 20G20

2. CJM 2012 (vol 65 pp. 1164)

Vitagliano, Luca
 Partial Differential Hamiltonian Systems We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson bracket, etc.. Unlike in standard multisymplectic approach to Hamiltonian field theory, in our formalism, the geometric structure (kinematics) and the dynamical information on the phase space'' appear as just different components of one single geometric object. Keywords:field theory, fiber bundles, multisymplectic geometry, Hamiltonian systemsCategories:70S05, 70S10, 53C80

3. CJM 2012 (vol 65 pp. 467)

Wilson, Glen; Woodward, Christopher T.
 Quasimap Floer Cohomology for Varying Symplectic Quotients We show that quasimap Floer cohomology for varying symplectic quotients resolves several puzzles regarding displaceability of toric moment fibers. For example, we (i) present a compact Hamiltonian torus action containing an open subset of non-displaceable orbits and a codimension four singular set, partly answering a question of McDuff, and (ii) determine displaceability for most of the moment fibers of a symplectic ellipsoid. Keywords:Floer cohomology, Hamiltonian displaceabilityCategory:53Dxx

4. CJM 2007 (vol 59 pp. 845)

Schaffhauser, Florent
 Representations of the Fundamental Group of an $L$-Punctured Sphere Generated by Products of Lagrangian Involutions In this paper, we characterize unitary representations of $\pi:=\piS$ whose generators $u_1, \dots, u_l$ (lying in conjugacy classes fixed initially) can be decomposed as products of two Lagrangian involutions $u_j=\s_j\s_{j+1}$ with $\s_{l+1}=\s_1$. Our main result is that such representations are exactly the elements of the fixed-point set of an anti-symplectic involution defined on the moduli space $\Mod:=\Hom_{\mathcal C}(\pi,U(n))/U(n)$. Consequently, as this fixed-point set is non-empty, it is a Lagrangian submanifold of $\Mod$. To prove this, we use the quasi-Hamiltonian description of the symplectic structure of $\Mod$ and give conditions on an involution defined on a quasi-Hamiltonian $U$-space $(M, \w, \mu\from M \to U)$ for it to induce an anti-symplectic involution on the reduced space $M/\!/U := \mu^{-1}(\{1\})/U$. Keywords:momentum maps, moduli spaces, Lagrangian submanifolds, anti-symplectic involutions, quasi-HamiltonianCategories:53D20, 53D30

5. CJM 2004 (vol 56 pp. 566)

Ni, Yilong
 Geodesics in a Manifold with Heisenberg Group as Boundary The Heisenberg group is considered as the boundary of a manifold. A class of hypersurfaces in this manifold can be regarded as copies of the Heisenberg group. The properties of geodesics in the interior and on the hypersurfaces are worked out in detail. These properties are strongly related to those of the Heisenberg group. Keywords:Heisenberg group, Hamiltonian mechanics, geodesicCategories:53C22, 53C17