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1. CJM Online first
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 reduction Categories:37J15, 70H33, 70F99, 37C80, 34C14, , 20G20 |
2. CJM 2008 (vol 60 pp. 685)
Closed and Exact Functions in the Context of Ginzburg--Landau Models For a general vector field we exhibit two Hilbert spaces, namely
the space of so called \emph{closed functions} and the space of \emph{exact functions}
and we calculate the codimension of the space of exact functions
inside the larger space of closed functions.
In particular we provide a new approach for the known cases:
the Glauber field and the second-order Ginzburg--Landau field
and for the case of the fourth-order Ginzburg--Landau field.
Keywords:Hermite polynomials, Fock space, Fourier coefficients, Fourier transform, group of symmetries Categories:42B05, 81Q50, 42A16 |
3. CJM 2004 (vol 56 pp. 638)
Multisymplectic Reduction for Proper Actions We consider symmetries of the Dedonder equation arising from
variational problems with partial derivatives. Assuming a proper
action of the symmetry group, we identify a set of reduced equations
on an open dense subset of the domain of definition of the fields
under consideration. By continuity, the Dedonder equation is
satisfied whenever the reduced equations are satisfied.
Keywords:Dedonder equation, multisymplectic structure, reduction,, symmetries, variational problems Categories:58J70, 35A30 |