14 citations · 48 across the 20 of their papers we have counts for
26 papers
Renormalization and blow ups for the nonlinear Schrödinger equation
Denis Gaidashev
Existence of finite-time blow ups in the classical one-dimensional nonlinear Schrödinger equation (NLS) (1) i \partial_t u + u_{x x} + |u|^{2r} u = 0, u(x,0) = u_0(x) has been one…
Wild attractors for Fibonacci maps
Artem Dudko, Denis Gaidashev
Existence of wild attractors -- attractors whose basin has a positive Lebesgue measure but is not a residual set -- has been one of central themes in one-dimensional dynamics. It h…
Renormalization and existence of the finite-time blow up solutions for a one-dimensional analogue of the Navier-Stokes equations
Denis Gaidashev, Alejandro Luque
The one-dimensional quasi-geostrophic equation is the one-dimensional Fourier-space analogue of the famous Navier-Stokes equations. In their work Li and Sinai have proposed a renor…
Universality but no rigidity for two-dimensional perturbations of almost commuting pairs
D. Gaidashev, D. Lilja
In this paper we consider two-dimensional dissipative maps of the annulus which are small perturbations of one-dimensional critical circle maps. It has been shown earlier that such…
Renormalization and a-priori bounds for Leray self-similar solutions to the generalized mild Navier-Stokes equations
Denis Gaidashev
We demonstrate that the problem of existence of Leray self-similar blow up solutions in a generalized mild Navier-Stokes system with the fractional Laplacian can be st…
Complex a priori bounds for Lorenz maps
Denis Gaidashev, Igors Gorbovickis
We construct complex a-priori bounds for certain infinitely renormalizable Lorenz maps. As a corollary, we show that renormalization is a real-analytic operator on the correspondin…