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.
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