Article ID Journal Published Year Pages File Type
1897376 Physica D: Nonlinear Phenomena 2010 11 Pages PDF
Abstract

The present paper studies the escape mechanism in collinear three point mass systems with small-range-repulsive/large-range-attractive pairwise interaction. Specifically, we focus on the asymptotic behaviour for systems with non-negative total energy.On the zero energy level set there are two distinct asymptotic states, called 1+1+11+1+1escape configurations  , where all the three separations infinitely increase as t→∞t→∞. We show that 1+1+11+1+1 escapes are improbable by proving that the set of initial conditions leading to such asymptotic configurations has zero Lebesgue measure. When the outer mass points are of the same kind we deduce the existence of a heteroclinic orbit connecting the 1+1+11+1+1 escape configurations. We further prove that this orbit is stable under parameter perturbation.In the positive energies’ case, we show that the set of initial conditions leading to 1+1+11+1+1 escape configurations has positive Lebesgue measure.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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