Computer Science
Scientific paper
Aug 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978cemec..18..195c&link_type=abstract
Celestial Mechanics, vol. 18, Aug. 1978, p. 195-204.
Computer Science
5
Hamiltonian Functions, Orbit Calculation, Orbital Mechanics, Integral Calculus, Motion Stability, Resonance
Scientific paper
It is noted that integrable cases containing 'singular' periodic orbits and islands have been known for a long time, that it has not been clear whether second- and higher-order islands normally appear in integrable systems, and that the presence of higher-order islands has sometimes been regarded as an indication of nonintegrability. This paper demonstrates that higher-order islands appear quite naturally in integrable systems, if some complexity is assumed, and that the appearance of higher-order islands around main resonant islands is not an indication of nonintegrability. Some examples of integrable systems with higher-order islands on a surface of section are given. It is shown how systems with higher-order resonances (which produce the higher-order islands) can be constructed in a general way.
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