M-FURCATIONS IN COUPLED MAPS

Author:

KIM SANG-YOON1

Affiliation:

1. Department of Physics, Kangwon National University, Chunchon, Kangwon-Do 200–701, Korea

Abstract

We study the scaling behavior of M-furcation (M=2, 3, 4,…) sequences of Mn-periodic(n=1, 2, …) orbits in two coupled one-dimensional (1D) maps. Using a renormalization method, how the scaling behavior depends on M is particularly investigated in the zero-coupling case in which the two 1D maps become uncoupled. The zero-coupling fixed map of the M-furcation renormalization transformation is found to have three relevant eigenvalues δ, α, and M (δ and α are the parameter and orbital scaling factors of 1D maps, respectively). Here the second and third ones, a and M, called the “coupling eigenvalues”, govern the scaling behavior of the coupling parameter, while the first one δ governs the scaling behavior of the nonlinearity parameter like in the case of 1D maps. The renormalization results are also confirmed by a direct numerical method.

Publisher

World Scientific Pub Co Pte Lt

Subject

Condensed Matter Physics,Statistical and Nonlinear Physics

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