Critical Attractor and Universality in a Renormalization Scheme for Three Frequency Hamiltonian Systems
arXiv:chao-dyn/9807007 · doi:10.1103/PhysRevLett.81.5125
Abstract
We study an approximate renormalization-group transformation to analyze the breakup of invariant tori for three degrees of freedom Hamiltonian systems. The scheme is implemented for the spiral mean torus. We find numerically that the critical surface is the stable manifold of a critical nonperiodic attractor. We compute scaling exponents associated with this fixed set, and find that they can be expected to be universal.
4 pages, 3 figures, REVTeX
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Cited by in corpus (5)
- Fractal Weyl Law for Open Chaotic Maps
- An approximate renormalization-group transformation for Hamiltonian systems with three degrees of freedom
- Aspects of Two-Level Systems under External Time Dependent Fields
- Approximate renormalization for the break-up of invariant tori with three frequencies
- KAM--renormalization-group for Hamiltonian systems with two degrees of freedom