A Method to Construct Asymptotic Solutions Invariant under the Renormalization Group

A renormalization group method with the Lie symmetry is presented for the singular perturbation problems. Asymptotic solutions are obtained as group-invariant solutions under approximate Lie group admitted by perturbed differential equations.Comment: 9 pages, 1 figur

Renormalization Analysis of Resonance Structure in 2-D Symplectic Map

A symplecticity-preserving RG analysis is carried out to study a resonance structure near an elliptic fixed point of a proto-type symplectic map in two dimensions. Through analyzing fixed points of a reduced RG map, a topology of the resonance structure such as a chain of resonant islands can be determined analytically. An application of this analysis to the Henon map is also presented.Comment: 10 page

Random Wandering Around Homoclinic-like Manifolds in Symplectic Map Chain

We present a method to construct a symplecticity preserving renormalization group map of a chain of weakly nonlinear symplectic maps and obtain a general reduced symplectic map describing its long-time behaviour. It is found that the modulational instability in the reduced map triggers random wandering of orbits around some homoclinic-like manifolds, which is understood as the Bernoulli shifts.Comment: submitted to Prog. Theor. Phy