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arXiv · 1711.03773

Symmetric Liapunov center theorem for minimal orbit

Ernesto Pérez-Chavela·Sławomir Rybicki·Daniel Strzelecki
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Abstract

Using the techniques of equivariant bifurcation theory we prove the existence of non-stationary periodic solutions of $\Gamma$-symmetric systems $\ddot q(t)=-\nabla U(q(t))$ in any neighborhood of an isolated orbit of minima $\Gamma(q_0)$ of the potential $U$. We show the strength of our result by proving the existence of new families of periodic orbits in the Lennard-Jones two- and three-body problems and in the Schwarzschild three-body problem.

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Ernesto Pérez-Chavela, Sławomir Rybicki, Daniel Strzelecki. 2017-11-10. Symmetric Liapunov center theorem for minimal orbit. https://arxiv.org/abs/1711.03773

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