MISC

2008年2月29日

Renormalization group in difference systems

Journal of Physics A: Mathematical and Theoretical
  • M. Iwasa
  • ,
  • K. Nozaki

41
8
開始ページ
085204
終了ページ
記述言語
英語
掲載種別
DOI
10.1088/1751-8113/41/8/085204

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. © 2008 IOP Publishing Ltd.

リンク情報
DOI
https://doi.org/10.1088/1751-8113/41/8/085204

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