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Analytic continuation in the case of non-regular dependency on a small parameter with an application to celestial mechanics

Author
Cors, J.; Pinyol, C.; Soler, J.
Type of activity
Journal article
Journal
Journal of differential equations
Date of publication
2005-12
Volume
219
Number
1
First page
1
Last page
19
DOI
https://doi.org/10.1016/j.jde.2005.07.027 Open in new window
URL
http://www.sciencedirect.com/science/article/pii/S0022039605002780 Open in new window
Abstract
We consider a non-autonomous system of ordinary differential equations. Assume that the time dependence is periodic with a very high frequency 1/¿, where ¿ is a small parameter and differentiability with respect to the parameter is lost when ¿ equals zero. We derive from Arenstorf's implicit function theorem a set of conditions to show the existence of periodic solutions. These conditions look formally like the standard analytic continuation method, namely, checking that a certain minor does ...
Keywords
Averaging, Continuation method, Periodic orbits, Spatial restricted three body problem, Symmetric orbits

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