C. Chandre, H.R. Jauslin, G. Benfatto, A. Celletti
An approximate renormalization-group transformation for Hamiltonian
systems with three degrees of freedom
(503K, REVTeX with 7 PS figures)
ABSTRACT. 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.