English

Dynamical convexity of the Euler problem of two fixed centers

Symplectic Geometry 2017-07-07 v3 Dynamical Systems

Abstract

We give thorough analysis for the rotation functions of the critical orbits from which one can understand bifurcations of periodic orbits. Moreover, we give explicit formulas of the Conley-Zehnder indices of the interior and exterior collision orbits and show that the universal cover of the regularized energy hypersurface of the Euler problem is dynamically convex for energies below the critical Jacobi energy.

Keywords

Cite

@article{arxiv.1601.02045,
  title  = {Dynamical convexity of the Euler problem of two fixed centers},
  author = {Seongchan Kim},
  journal= {arXiv preprint arXiv:1601.02045},
  year   = {2017}
}

Comments

Final version, title changed, to appear in Math. Proc. Cambridge Philos. Soc

R2 v1 2026-06-22T12:25:54.960Z