On the small divisors. I - The convergence of the modified Zeipel's series and the resonant quasi-periodic solutions

Details On the small divisors. I - The convergence of the modified Zeipel's series and the resonant quasi-periodic solutions On the small divisors. I - The convergence of the modified Zeipel's series and the resonant quasi-periodic solutions

Jul 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..27..225m&link_type=abstract

Celestial Mechanics, vol. 27, July 1982, p. 225-265. In French.

Computer Science

2

Celestial Mechanics, Orbit Perturbation, Periodic Functions, Resonance, Series Expansion, Von Zeipel Method, Convergence, Differential Equations, Theorem Proving

Scientific paper

The convergence of a modification of the Zeipel series of frequencies fixed in advance, which takes into account short period perturbations of the right-hand members of the differential equations of celestial mechanics, is demonstrated. By using these series, the existence of quasi-periodic resonant solutions that require no complementary parameters is established.

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