Journal
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
Volume 18, Issue 3, Pages 969-986Publisher
SPRINGER BASEL AG
DOI: 10.1007/s12346-019-00322-y
Keywords
Periodic solutions; Averaging theory; Anisotropic Manev problem; Hydrogen atom problem
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In this paper we use the averaging theory for studying the periodic solutions of the planar anisotropic Manev problem and of two perturbations of the hydrogen atom problem. When a convenient parameter is sufficiently small we prove that for every value e is an element of (0,1) a unique elliptic periodic solution with eccentricity e of the Kepler problem can be continued to the mentioned three problems.
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