A multiscale asymptotic analysis of time evolution equations on the complex plane
- Departamento de Ciências do Mar, Universidade Federal de São Paulo, Rua Dr. Carvalho de Mendonça 144, 11070-100 Santos, SP (Brazil)
Using an appropriate norm on the space of entire functions, we extend to the complex plane the renormalization group method as developed by Bricmont et al. The method is based upon a multiscale approach that allows for a detailed description of the long time asymptotics of solutions to initial value problems. The time evolution equation considered here arises in the study of iterations of the block spin renormalization group transformation for the hierarchical N-vector model. We show that, for initial conditions belonging to a certain Fréchet space of entire functions of exponential type, the asymptotics is universal in the sense that it is dictated by the fixed point of a certain operator acting on the space of initial conditions.
- OSTI ID:
- 22596594
- Journal Information:
- Journal of Mathematical Physics, Vol. 57, Issue 7; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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