3 papers
math.DS2026
Rotation domains for maps of bounded type
Nataliya Goncharuk, Michael Yampolsky
We present a novel approach for deriving KAM-type linearization theorems directly -- and almost immediately -- from the existence of the stable foliation for a renormalization oper…
math.DS2024
Authomorphic measures with negative exponents for multicritical circle maps
Nataliya Goncharuk, Michael Yampolsky
Authomorphic or -measures for circle diffeomorphisms were introduced by R.Douady and J.-C. Yoccoz in 1999. They have multiple applications in circle dynamics, with the case $s=-…
math.DS1996
Geography of the cubic connectedness locus I: Intertwining surgery
Adam L. Epstein, Michael Yampolsky
We exhibit products of Mandelbrot sets in the two-dimensional complex parameter space of cubic polynomials. These products were observed by J. Milnor in computer experiments which…