19 citations · 62 across the 27 of their papers we have counts for
31 papers
A simple proof of Sullivan's complex bounds
Genadi Levin
About 35 years ago Dennis Sullivan proved a precompactness property ("complex bounds") for infinitely renormalizable real quadratic polynomials with bounded combinatorics. We prese…
Polynomial-like dynamics of analytic maps
Genadi Levin
The theory of polynomial-like maps is of fundamental importance in holomorphic dynamics. We study dynamical properties of a larger class of maps. Our main result is that, under som…
On invariant line fields of rational functions
Genadi Levin
Adopting the approach of [7] we study rational function carrying invariant line fields on the Julia set. In particular, we show that under certain weak conditions all possible meas…
On symmetries of the IFS attractor
Genadi Levin
We apply some methods and technique of complex dynamics to study the set of symmetries of attractors of holomorphic Iterated Function Systems (IFS), as well as relations between IF…
On invariant measures of "satellite" infinitely renormalizable quadratic polynomials
Genadi Levin, Feliks Przytycki
Let f(z)=z^2+c be an infinitely renormalizable quadratic polynomial and J_\infty be the intersection of forward orbits of "small" Julia sets of its simple renormalizations. We prov…
Maps with no a priori bounds
Alexander Blokh, Genadi Levin, Lex Oversteegen +1
The modulus of a polynomial-like (PL) map is an important invariant that controls distortion of the straightening map and, hence, geometry of the corresponding PL Julia set. Lower…