# An Estimation for the Hyperbolic Region of Elliptic Lagrangian Solutions in the Planar Three-body Problem

*2013, Volume 18, Number 6, pp. 732-741*

Author(s):

**Hu X., Ou Y.**

It is well known that the linear stability of elliptic Lagrangian solutions depends on the mass parameter $\beta = 27(m_1m_2+m_2m_3+m_3m_1)/(m_1+m_2+m_3)^2 \in [0,9]$ and the eccentricity $e \in [0,1)$. Based on new techniques for evaluating the hyperbolicity and the recently developed trace formula for Hamiltonian systems [9], we identify regions for $(\beta,e)$ such that elliptic Lagrangian solutions are hyperbolic. Consequently, we have proven that the elliptic relative equilibrium of square central configurations is hyperbolic with any eccentricity.

Access to the full text on the Springer website |