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The Conley–Zehnder indices of the rotating Kepler problem

Published online by Cambridge University Press:  03 October 2012

PETER ALBERS
Affiliation:
Mathematisches Institut, Büro 308Westfälische Wilhelms-Universität MünsterEinsteinstrasse 62, D-48149 Münster, Germany. e-mail: peter.albers@uni-muenster.de
JOEL W. FISH
Affiliation:
Max Planck InstituteInselstrasse 22, D-04103 Leipzig, Germany. e-mail: joel.fish@mis.mpg.de
URS FRAUENFELDER
Affiliation:
Department of Mathematics and Research Institute of Mathematics, Seoul National University, Building 27, room 403 San 56-1, Sillim-dong, Gwanak-gu, Seoul 151-747, South Korea. e-mail: frauenf@snu.ac.kr
OTTO VAN KOERT
Affiliation:
Department of Mathematics and Research Institute of MathematicsSeoul National University, Building 27, room 402 San 56-1, Sillim-dong, Gwanak-gu, Seoul 151-747, South Korea. e-mail: okoert@snu.ac.kr

Abstract

We determine the Conley–Zehnder indices of all periodic orbits of the rotating Kepler problem for energies below the critical Jacobi energy. Consequently, we show the universal cover of the bounded component of the regularized energy hypersurface is dynamically convex. Moreover, in the universal cover there is always precisely one periodic orbit with Conley–Zehnder index 3, namely the lift of the doubly covered retrograde circular orbit.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2012

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References

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