We prove the presence of chaotic dynamics for the classical two-body Kepler problem with a time-periodic gravitational coefficient oscillating between two fixed values. The set of chaotic solutions we detect is coded by the number of revolutions in each period.
The chaotic dynamics is obtained for large period T as well as for small angular momentum μ. In particular, we provide an explicit lower bound on T and explicit upper bound on μ which guarantee the existence of complex dynamics.
We get our results by applying a simple and well-known topological method, the stretching along the path technique. Our results are robust with respect to small perturbations of the gravitational coefficient and to the addition of a small friction term.
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The first author was supported by Fundação para a Ciência e Tecnologia
through projects UID/MAT/ 04561/2013 and PTDC/MAT/113383/2009. The second author was supported by
Ministerio de Economía y Competitividad (Spain) through project MTM2014-52232-P.
Advanced Nonlinear Studies (ANS) is aimed at publishing scholarly articles on nonlinear problems, particularly those involving Differential and Integral Equations, Dynamical Systems, Calculus of Variations, and related areas. It will also publish novel and interesting applications of these areas to problems in biology, engineering, materials sciences, physics and other sciences.