A Renormalization Group for Hamiltonians: Numerical Results

Details A Renormalization Group for Hamiltonians: Numerical Results A Renormalization Group for Hamiltonians: Numerical Results

1998-04-17

arxiv.org/abs/chao-dyn/9804030v1

Nonlinear Sciences

Chaotic Dynamics

11 Pages, 2 Figures. For future updates, check ftp://ftp.ma.utexas.edu/pub/papers/koch/

Scientific paper

10.1088/0951-7715/11/5/001

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.

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