22 citations · 108 across the 45 of their papers we have counts for
55 papers
Ulam meets Turing: constructing quadratic maps with non-computable SRB measures
Cristóbal Rojas, Michael Yampolsky
In 1946, S. Ulam invented Monte Carlo method, which has since become the standard numerical technique for making statistical predictions for long-term behaviour of dynamical system…
Renormalization of circle maps and smoothness of Arnold tongues
Nataliya Goncharuk, Michael Yampolsky
We study the global behavior of the renormalization operator on a specially constructed Banach manifold that has cubic critical circle maps on its boundary and circle diffeomorphis…
Rigidity of analytic and smooth bi-cubic multicritical circle maps with bounded type rotation numbers
Igors Gorbovickis, Michael Yampolsky
We prove that if two analytic multicritical circle maps with the same bounded type rotation number are topologically conjugate by a conjugacy which matches the critical points of t…
Hyperbolicity of Renormalization for bi-cubic circle maps with bounded combinatorics
Gabriela Estevez, Michael Yampolsky
We construct a hyperbolic attractor of renormalization of bi-cubic circle maps with bounded combinatorics, with a codimension-two stable foliation.
KAM-renormalization and Herman rings for 2D maps
Michael Yampolsky
In this note, we extend the renormalization horseshoe we have recently constructed with N. Goncharuk for analytic diffeomorphisms of the circle to their small two-dimensional pertu…
Computability in Harmonic Analysis
Ilia Binder, Adi Glucksam, Cristobal Rojas +1
We study the question of constructive approximation of the harmonic measure of a connected bounded domain with respect to a point . In particular, using a new no…