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Renormalization Group on Wiener Space: Spectral Theory and Universality
André L. P. Considera, Alexei A. Mailybaev
We develop a rigorous renormalization group (RG) formalism on Wiener space. We introduce an RG operator acting on probability measures over continuous paths, whose fix…
RG analysis of spontaneous stochasticity on a fractal lattice: stability and bifurcations
Alexei A. Mailybaev
In this paper, we study the stability and bifurcations of spontaneous stochasticity using an approach reminiscent of the Feigenbaum renormalization group (RG). We consider dynamica…
Spontaneous stochasticity and renormalization group in discrete multi-scale dynamics
Alexei A. Mailybaev, Artem Raibekas
We introduce a class of multi-scale systems with discrete time, motivated by the problem of inviscid limit in fluid dynamics in the presence of small-scale noise. These systems are…
Hidden spatiotemporal symmetries and intermittency in turbulence
Alexei A. Mailybaev
We consider general infinite-dimensional dynamical systems with the Galilean and spatiotemporal scaling symmetry groups. Introducing the equivalence relation with respect to tempor…
Universal structure of blow-up in 1D conservation laws
Alexei A. Mailybaev
We discuss universality properties of blow-up of a classical (smooth) solutions of conservation laws in one space dimension. It is shown that the renormalized wave profile tends to…
Computation of multiple eigenvalues and generalized eigenvectors for matrices dependent on parameters
A. A. Mailybaev
The paper develops Newton's method of finding multiple eigenvalues with one Jordan block and corresponding generalized eigenvectors for matrices dependent on parameters. It compute…