Displaying similar documents to “Bound states in completely integrable systems with two types of particles”

Explicit geodesic graphs on some H-type groups

Dušek, Zdeněk

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A homogeneous Riemannian manifold M = G / H is called a “g.o. space” if every geodesic on M arises as an orbit of a one-parameter subgroup of G . Let M = G / H be such a “g.o. space”, and m an Ad ( H ) -invariant vector subspace of Lie ( G ) such that Lie ( G ) = m ⊕ Lie ( H ) . A is a map ξ : m → Lie ( H ) such that t ↦ exp ( t ( X + ξ ( X ) ) ) ( e H ) is a geodesic for every X ∈ m ∖ { 0 } . The author calculates explicitly such geodesic graphs for certain special 2-step nilpotent Lie groups. More precisely, he deals with “generalized Heisenberg groups” (also known as “H-type groups”) whose center has...

Non singular Hamiltonian systems and geodesic flows on surfaces with negative curvature.

Ernesto A. Lacomba, J. Guadalupe Reyes (1998)

Publicacions Matemàtiques

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We extend here results for escapes in any given direction of the configuration space of a mechanical system with a non singular bounded at infinity homogeneus potential of degree -1, when the energy is positive. We use geometrical methods for analyzing the parallel and asymptotic escapes of this type of systems. By using Riemannian geometry methods we prove under suitable conditions on the potential that all the orbits escaping in a given direction are asymptotically parallel among themselves....