Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1999-03-15
Phys. Rev. E 60, 5412 (1999).
Nonlinear Sciences
Chaotic Dynamics
10 pages typeset using REVTeX, 7 PS figures
Scientific paper
10.1103/PhysRevE.60.5412
We construct an approximate renormalization transformation that combines Kolmogorov-Arnold-Moser (KAM)and renormalization-group techniques, to analyze instabilities in Hamiltonian systems with three degrees of freedom. This scheme is implemented both for isoenergetically nondegenerate and for degenerate Hamiltonians. For the spiral mean frequency vector, we find numerically that the iterations of the transformation on nondegenerate Hamiltonians tend to degenerate ones on the critical surface. As a consequence, isoenergetically degenerate and nondegenerate Hamiltonians belong to the same universality class, and thus the corresponding critical invariant tori have the same type of scaling properties. We numerically investigate the structure of the attracting set on the critical surface and find that it is a strange nonchaotic attractor. We compute exponents that characterize its universality class.
Benfatto Giuseppe
Celletti Alessandra
Chandre Cristel
Jauslin Hans-Rudolf
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