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Renormalization group in difference systems. (English) Zbl 1155.39001
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.

39A05General theory of difference equations
81T17Renormalization group methods (quantum theory)
37J10Symplectic mappings, fixed points (dynamical systems)
37J20Bifurcation problems (finite-dimensional Hamiltonian etc. systems)
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