738 research outputs found
Straight Line Orbits in Hamiltonian Flows
We investigate periodic straight-line orbits (SLO) in Hamiltonian force
fields using both direct and inverse methods. A general theorem is proven for
natural Hamiltonians quadratic in the momenta in arbitrary dimension and
specialized to two and three dimension. Next we specialize to homogeneous
potentials and their superpositions, including the familiar H\'enon-Heiles
problem. It is shown that SLO's can exist for arbitrary finite superpositions
of -forms. The results are applied to a family of generalized H\'enon-Heiles
potentials having discrete rotational symmetry. SLO's are also found for
superpositions of these potentials.Comment: laTeX with 6 figure
Simultaneous Identification of the Diffusion Coefficient and the Potential for the Schr\"odinger Operator with only one Observation
This article is devoted to prove a stability result for two independent
coefficients for a Schr\"odinger operator in an unbounded strip. The result is
obtained with only one observation on an unbounded subset of the boundary and
the data of the solution at a fixed time on the whole domain
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