Renormalization group in difference systems
Abstract
A new singular perturbation method based on the Lie symmetry group is presented to a system of difference equations. This method yields consistent derivation of a renormalization group equation which gives an asymptotic solution of the difference equation. The renormalization group equation is a Lie differential equation of a Lie group which leaves the system approximately invariant. For a 2D symplectic map, the renormalization group equation becomes a Hamiltonian system and a long-time behaviour of the symplectic map is described by the Hamiltonian. We study the Poincaré-Birkoff bifurcation in the 2D symplectic map by means of the Hamiltonian and give a condition for the bifurcation.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- February 2008
- DOI:
- 10.1088/1751-8113/41/8/085204
- arXiv:
- arXiv:0801.3156
- Bibcode:
- 2008JPhA...41h5204I
- Keywords:
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- Nonlinear Sciences - Chaotic Dynamics;
- Condensed Matter - Other Condensed Matter
- E-Print:
- Accepted to J. Phys. A, 7 pages