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On Hausdorff dimension of oscillatory motions in three body problems
Hausdorff dimension oscillatory motions three body problems
2015/9/25
We show that for the Sitnikov example and for the restricted planar circular 3–body problem the set of oscillatory motions often has maximal Hausdorff dimension. Also, we construct Newhouse domains fo...
Lambert’s theorem, convex optimization, and minimizing solutions of the n-body problems
Lambert’s theorem convex optimization minimizing solutions n-body problems
2015/3/18
Lambert’s theorem, convex optimization, and minimizing solutions of the n-body problems.
Variational Minimizing Parabolic Orbits for the Restricted 3-Body Problems
Restricted 3-Body Problems Variational Minimizers Odd Parabolic Orbits
2011/10/26
The Least Action Principle is the simplest and the most nature rule in the world. Using variational minimizing methods and the implicit symmetries, we prove the existence of the odd symmetric paraboli...
Partial Answers on Saari’s Conjecture of N-body problems
N-body problems Relative equilibria Central configurations Variational methods
2011/10/13
One special periodic solution of the Newtonian N-body problems is relative equilibria,which rotates rigidly about their center of mass.In 1970,Donald G.Saari conjectured:if the moment of inertia of N-...