On the Lyapunov instability in Newtonian dynamics

2019/06/27 by Burgos, Juan Manuel, Maderna, Ezequiel, Paternain, Miguel
#37J25 70H14 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.11962

Abstract

We prove Lyapunov instability for cases in which the local minimum of the potential energy is reached on a hypersurface of the configuration space. In contrast to the known results in this direction, which hold for potentials satisfying hypotheses in the first non-zero jet, this new result covers several real analytic cases that the previous ones do not.

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