14 citations · 48 across the 20 of their papers we have counts for
21 papers · 1 filter
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…
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…
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…
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. de…
Exponentially small splitting of separatrices near a period-doubling bifurcation in area-preserving maps
Denis Gaidashev, Marina Gonchenko
We consider the conservative Hénon family at the period-doubling bifurcation of its fixed point and demonstrate that the separatrices of the fixed saddle point nearing the bifurcat…
Renormalization and Siegel disks for complex Hénon maps
Denis Gaidashev, Remus Radu, Michael Yampolsky
We use hyperbolicity of golden-mean renormalization of dissipative Hénon-like maps to prove that the boundaries of Siegel disks of sufficiently dissipative quadratic complex Hénon…