The near-resonance theorem: analysis of the vicinity of periodic solutions of analytic differential systems.

Details The near-resonance theorem: analysis of the vicinity of periodic solutions of analytic differential systems. The near-resonance theorem: analysis of the vicinity of periodic solutions of analytic differential systems.

Jan 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988ltdb.conf..427m&link_type=abstract

NATO Advanced Study Institute on Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems, p. 427 - 448

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Resonances: Periodic Orbits, Stability: Periodic Orbits

Scientific paper

The near-resonance theorem allows to simplify the systems of differential equations and to study the vicinity and the stability of their periodic solutions. It leads to suitable transformations that cancel all non-near-resonant terms, even those of very large orders. The demonstration of the theorem is difficult but short and various applications are presented.

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