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Maslov-Type Indices and Linear Stability of Elliptic Euler Solutions of the Three-Body Problem

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Abstract

In this paper, we use the central configuration coordinate decomposition to study the linearized Hamiltonian system near the 3-body elliptic Euler solutions. Then using the Maslov-type \({\omega}\)-index theory of symplectic paths and the theory of linear operators we compute the \({\omega}\)-indices and obtain certain properties of linear stability of the Euler elliptic solutions of the classical three-body problem.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, Zhejiang, China

    Qinglong Zhou

  2. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, China

    Yiming Long

  3. Beijing Advanced Innovation Center for Imaging Technology, Capital Normal University, Beijing, 100048, China

    Yiming Long

Authors
  1. Qinglong Zhou
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  2. Yiming Long
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Corresponding author

Correspondence to Qinglong Zhou.

Additional information

Communicated by P. Rabinowitz

Qinglong Zhou: Partially supported by NSFC (Nos. 11501330, 11425105) and CPSF (No. 2015M582071) of China.

Yiming Long: Partially supported by NSFC (Nos. 11131004, 11671215), LPMC of MOE of China, Nankai University, and BAICIT at Capital Normal University.

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Zhou, Q., Long, Y. Maslov-Type Indices and Linear Stability of Elliptic Euler Solutions of the Three-Body Problem. Arch Rational Mech Anal 226, 1249–1301 (2017). https://doi.org/10.1007/s00205-017-1154-8

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  • DOI: https://doi.org/10.1007/s00205-017-1154-8

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