Uses of Envelopes for Global and Asymptotic Analysis; geometrical meaning of renormalization group equation

1997/09/20 by Teiji Kunihiro, Kunihiro, Teiji
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Opinion Dynamics and Social Influence #Pattern Formation and Solitons (nlin.PS) #Quantum chaos and dynamical systems

paper · doi:10.48550/arxiv.patt-sol/9709003

openalex publication_date 1997/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We give a comprehensive review of the renormalization group method for global and asymptotic analysis, putting an emphasis on the relevance to the classical theory of envelopes and the existence of invariant manifolds of the dynamics under consideration. We clarify that an essential point of the method is to convert the problem from solving differential equations to obtaining suitable initial (or boundary) conditions. We mention that the notion of envelopes is also useful for constructing global and asymptotic behavior of wave functions of quantum systems such as the ones with the quartic potential or double-well potential.

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