Miguel Ángel González León

Orbits in the problem of two fixed centers on the sphere

A trajectory isomorphism between the two Newtonian fixed center problem in the sphere and two associated planar two fixed center problems is constructed by performing two simultaneous gnomonic projections in S2. This isomorphism converts the original quadratures into elliptic integrals and allows the bifurcation diagram of the spherical problem to be analyzed in terms of the corresponding ones of the planar systems. The dynamics along the orbits in the different regimes for the problem in S2 is expressed in terms of Jacobi elliptic functions.

Solitary Waves in Massive Nonlinear S N -Sigma Models ?

The solitary waves of massive (1+1)-dimensional nonlinear S N -sigma models are unveiled. It is shown that the solitary waves in these systems are in one-to-one correspon- dence with the separatrix trajectories in the repulsive N-dimensional Neumann mechanical problem. There are topological (heteroclinic trajectories) and non-topological (homoclinic trajectories) kinks. The stability of some embedded sine-Gordon kinks is discussed by means of the direct estimation of the spectra of the second-order fluctuation operators around them, whereas the instability of other topological and non-topological kinks is established applying the Morse index theorem.