A Renormalization Group for Hamiltonians: Numerical Results
arXiv:chao-dyn/9804030 · doi:10.1088/0951-7715/11/5/001
Abstract
We describe a renormalization group transformation that is related to the breakup of golden invariant tori in Hamiltonian systems with two degrees of freedom. This transformation applies to a large class of Hamiltonians, is conceptually simple, and allows for accurate numerical computations. In a numerical implementation, we find a nontrivial fixed point and determine the corresponding critical index and scaling. Our computed values for various universal constants are in good agreement with existing data for area-preserving maps. We also discuss the flow associated with the nontrivial fixed point.
11 Pages, 2 Figures. For future updates, check ftp://ftp.ma.utexas.edu/pub/papers/koch/
References in corpus (3)
Cited by in corpus (11)
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- An approximate renormalization-group transformation for Hamiltonian systems with three degrees of freedom
- Critical Attractor and Universality in a Renormalization Scheme for Three Frequency Hamiltonian Systems
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- Rigidity for infinitely renormalizable area-preserving maps
- Scaling law for the critical function of an approximate renormalization
- Strange attractor for the renormalization flow for invariant tori of Hamiltonian systems with two generic frequencies
- Period Doubling Renormalization for Area-Preserving Maps and Mild Computer Assistance in Contraction Mapping Principle
- Application of renormalization to the dynamics of a particle in a infinite square-well potential driven by an external field
- Period Doubling in Area-Preserving Maps: An Associated One Dimensional Problem
- KAM--renormalization-group for Hamiltonian systems with two degrees of freedom