Regularized Renormalization Group Reduction of Symplectic Map

Details Regularized Renormalization Group Reduction of Symplectic Map Regularized Renormalization Group Reduction of Symplectic Map

2000-08-10

arxiv.org/abs/nlin/0008013v1

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1143/JPSJ.70.49

By means of the perturbative renormalization group method, we study a long-time behaviour of some symplectic discrete maps near elliptic and hyperbolic fixed points. It is shown that a naive renormalization group (RG) map breaks the symplectic symmetry and fails to describe a long-time behaviour. In order to preserve the symplectic symmetry, we present a regularization procedure, which gives a regularized symplectic RG map describing an approximate long-time behaviour succesfully.

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