6533b7d0fe1ef96bd125adee
RESEARCH PRODUCT
Kolmogorov-Arnold-Moser–Renormalization-Group Analysis of Stability in Hamiltonian Flows
Cristel ChandreHans-rudolf JauslinM. Govinsubject
PhysicsKolmogorov–Arnold–Moser theoremFOS: Physical sciencesGeneral Physics and AstronomyTorusRenormalization groupFixed pointNonlinear Sciences - Chaotic DynamicsUniversality (dynamical systems)Renormalizationsymbols.namesakeQuantum mechanicsPhase spacesymbolsChaotic Dynamics (nlin.CD)Hamiltonian (quantum mechanics)Mathematics::Symplectic GeometryMathematical physicsdescription
We study the stability and breakup of invariant tori in Hamiltonian flows using a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. We implement the scheme numerically for a family of Hamiltonians quadratic in the actions to analyze the strong coupling regime. We show that the KAM iteration converges up to the critical coupling at which the torus breaks up. Adding a renormalization consisting of a rescaling of phase space and a shift of resonances allows us to determine the critical coupling with higher accuracy. We determine a nontrivial fixed point and its universality properties.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1997-11-17 | Physical Review Letters |