A Renormalization Group for Hamiltonians: Numerical Results
chao-dyn
2009-10-31 v1 Chaotic Dynamics
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.
Cite
@article{arxiv.chao-dyn/9804030,
title = {A Renormalization Group for Hamiltonians: Numerical Results},
author = {Juan J. Abad and Hans Koch and Peter Wittwer},
journal= {arXiv preprint arXiv:chao-dyn/9804030},
year = {2009}
}
Comments
11 Pages, 2 Figures. For future updates, check ftp://ftp.ma.utexas.edu/pub/papers/koch/