Satoru KUROSAKI

Department of Applied Physics
School of Science and Engineering
Waseda University
3-4-1, Okubo Shinjuku-ku Tokyo 169, JAPAN
kurosaki@aizawa.phys.waseda.ac.jp 
 
 

The breakup of KAM tori and diffusion in four-dimensional symplectic maps

Abstract : The breakup of KAM tori in four-dimensional symplectic maps is studied. KAM tori are constructed explicitly by the conjugation technique. The succession to the breakup depends on the perturbations which determine the dominant type of small divisors in the conjugation function. The secular component of orbits is sensitive to the breakup of KAM tori close to it. We construct the resonance structure on the frequency plane based on that observation. The resonance structure is related to the Arnold web. The region fulfilled by KAM tori prevents orbits diffusing but elliptic normal modes do not.