Approximation of center manifolds on the renormalization group method

The renormalization group (RG) method for differential equations is one of the perturbation methods for obtaining approximate solutions. This article shows that the RG method is effectual for obtaining an approximate center manifold and an approximate flow on it when applied to equations having a center manifold.

[1]  Neil Fenichel.  Persistence and Smoothness of Invariant Manifolds for Flows , 1971 .

[2]  The Renormalization-Group Method Applied to Asymptotic Analysis,of Vector Fields , 1996, hep-th/9609045.

[3]  B. Mudavanhu,et al.  A Renormalization Group Method for Nonlinear Oscillators , 2001 .

[4]  Anthony Harkin,et al.  Analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations , 2008 .

[5]  Oono,et al.  Renormalization group theory for global asymptotic analysis. , 1994, Physical review letters.

[6]  T. Kunihiro.  A geometrical formulation of the renormalization group method for global analysis II: Partial differential equations , 1995, patt-sol/9508001.

[7]  Hayato Chiba,et al.  C1 Approximation of Vector Fields Based on the Renormalization Group Method , 2008, SIAM J. Appl. Dyn. Syst..

[8]  Oono,et al.  Renormalization group and singular perturbations: Multiple scales, boundary layers, and reductive perturbation theory. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  S. Wiggins.  Normally Hyperbolic Invariant Manifolds in Dynamical Systems , 1994 .

[10]  Robert E. O'Malley,et al.  A New Renormalization Method for the Asymptotic Solution of Weakly Nonlinear Vector Systems , 2003, SIAM J. Appl. Math..

[11]  J. Carr.  Applications of Centre Manifold Theory , 1981 .

[12]  M. Ziane.  On a certain renormalization group method , 2000 .

[13]  E. Kirkinis.  The renormalization group and the implicit function theorem for amplitude equations , 2008 .

[14]  Michael Shub,et al.  The local theory of normally hyperbolic, invariant, compact manifolds , 1977 .

[15]  Shin-ichiro Ei,et al.  Renormalization-Group Method for Reduction of Evolution Equations; Invariant Manifolds and Envelopes , 2000 .