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- Title
Dynamical convexity of the Euler problem of two fixed centers.
- Authors
KIM, SEONGCHAN
- 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 regularised energy hypersurface of the Euler problem is dynamically convex for energies below the critical Jacobi energy.
- Subjects
CONVEX domains; MATHEMATICAL functions; HYPERSURFACES; JACOBI varieties; MATHEMATICAL formulas
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2018, Vol 165, Issue 2, p359
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004117000548