Geometric proof of strong stable/unstable manifolds with application to the restricted three body problem
DOI:
https://doi.org/10.12775/TMNA.2015.051Keywords
Invariant manifolds, center manifolds, fixed pointsAbstract
We present a method for establishing strong stable/unstable manifolds of fixed points for maps and ODEs. The method is based on cone conditions, suitably formulated to allow for application in computer assisted proofs. In the case of ODEs, assumptions follow from estimates on the vector field, and it is not necessary to integrate the system. We apply our method to the restricted three body problem and show that for a given choice of the mass parameter, there exists a homoclinic orbit along matching strong stable/unstable manifolds of one of the libration points.Downloads
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2015-09-01
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CAPIŃSKI, Maciej J. and WASIECZKO-ZAJĄC, Anna. Geometric proof of strong stable/unstable manifolds with application to the restricted three body problem. Topological Methods in Nonlinear Analysis. Online. 1 September 2015. Vol. 46, no. 1, pp. 363 - 399. [Accessed 23 April 2024]. DOI 10.12775/TMNA.2015.051.
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