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Dynamical convexity of the Euler problem of two fixed centers

Published online by Cambridge University Press:  24 July 2017

SEONGCHAN KIM
SEONGCHAN KIM*
Affiliation:
Institut für Mathematik, Universität Augsburg, Raum L1-2030, Universitätsstrasse 14, D-86159 Augsburg, Germany. e-mail: seongchan.kim@math.uni-augsburg.de
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 165 , Issue 2 , September 2018 , pp. 359 - 384
Copyright
Copyright © Cambridge Philosophical Society 2017 

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