3 papers
math.DS2025
On the geometry of period doubling invariant sets for area-preserving maps
Denis Gaidashev, Dan Lilja
The geometry of the period doubling Cantor sets of strongly dissipative infinitely renormalizable Hénon-like maps has been shown to be unbounded by M. Lyubich, M. Martens and A. d…
math.AP2025
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…
math.DS2024
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…