6533b85efe1ef96bd12bf420
RESEARCH PRODUCT
Approximate renormalization-group transformation for Hamiltonian systems with three degrees of freedom
Giuseppe BenfattoCristel ChandreHans-rudolf JauslinA. Cellettisubject
KAM TORI; RENORMALIZATION GROUP; STRANGE ATTRACTORSDegenerate energy levelsFOS: Physical sciencesKAM TORIRenormalization groupNonlinear Sciences - Chaotic DynamicsStrange nonchaotic attractorSTRANGE ATTRACTORSHamiltonian systemNonlinear Sciences::Chaotic DynamicsRenormalizationTransformation (function)RENORMALIZATION GROUPQuantum mechanicsChaotic Dynamics (nlin.CD)Invariant (mathematics)Settore MAT/07 - Fisica MatematicaMathematics::Symplectic GeometryScalingMathematicsMathematical physicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1999-03-15 | Physical Review E |