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2013
Impact Factor

Xijun Hu

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

Publications:

 Hu X., Ou Y. An Estimation for the Hyperbolic Region of Elliptic Lagrangian Solutions in the Planar Three-body Problem 2013, vol. 18, no. 6, pp.  732-741 Abstract 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 DOI:10.1134/S1560354713060129