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Zbl 1155.39001
Iwasa, M.; Nozaki, K.
Renormalization group in difference systems. (English)
[J] J. Phys. A, Math. Theor. 41, No. 8, Article ID 085204, 7 p. (2008). ISSN 1751-8113; ISSN 1751-8121/e

The authors present another normalization group method in terms of the Lie symmetry group. Without calculating a naive perturbation solution, the normalized solution is constructed as an invariant solution under transformation which leaves the system approximately invariant. For a 2D symplectic map, the normalization group equation becomes a Hamiltonian system and a long-time behaviour of the symplectic map is described by the Hamiltonian. The Poincaré-Birkhoff bifurcation in the 2D symplectic map is studied by means of the Hamiltonian and a condition for bifurcation is given.
[Bolis Basit (Clayton)]

MSC 2000:: *39A05 General theory of difference equations
81T17 Renormalization group methods
37J10 Symplectic mappings, fixed points
37J20 Bifurcation problems

Keywords: normalization group method; Lie symmetry group; Hamiltonian system; symplectic map; Poincaré-Birkhoff bifurcation

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