Yuwei Ou

Jinan, Shandong 250100, The People’s Republic of China
Department of Mathematics, Shandong University


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.
Keywords: central configurations, elliptic relative equilibrium, linear stability, hyperbolicity, $n$-body problem
Citation: Hu X., Ou Y.,  An Estimation for the Hyperbolic Region of Elliptic Lagrangian Solutions in the Planar Three-body Problem, Regular and Chaotic Dynamics, 2013, vol. 18, no. 6, pp. 732-741

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