A method for analytically representing area-preserving mappings |
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Institution: | Moscow, Russia;Moscow, Russia;Facultad de C.C. Matemáticas, Universidad Complutense de Madrid, Madrid 28040, Spain;Moscow, Russia;St Petersburg, Russia;Samara, Russia;Cheboksary, Russia |
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Abstract: | An area-preserving mapping is considered. It is assumed that the mapping has a fixed point and is analytic in a small neighbourhood near it. A constructive algorithm for obtaining a representation of the mapping in the form of a composite of two area-preserving mappings, one of which is a nearly identity mapping, while the other corresponds to the real normal form of a linearized mapping, is described. The algorithm is used in the problem of the stability of the translational motion of a rigid body in a uniform gravitational field when it undergoes collisions with a fixed horizontal plane and in the problem of the stability of one type of resonant in-plane rotations of a satellite, i.e., a rigid body, in an elliptic orbit. |
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