Add to ORKGLet 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 prove that if f admits an infinite sequence of satellite renormalizations, then every invariant measure of f: J_\infty\to J_\infty is supported on the postcritical set and has zero Lyapunov exponent. Coupled with [G. Levin, F. Przytycki, W. Shen, The Lyapunov exponent of holomorphic maps. Invent. Math. 205 (2016), 363-382], this implies that the Lyapunov exponent of such f at c is equal to zero, which answers partly a question posed by Weixiao Shen.Comment: 1 figure. Comments are welcom
In this paper geometric properties of infinitely renormalizable real Henon-like maps F in R-2 are st...
Let f be a real rational function with all critical points on the extended real axis and of even ord...
Since its inception in the 1970s at the hands of Feigenbaum and, independently, Coullet and Tresser ...
Let f be an infinitely-renormalizable quadratic polynomial and J_\infty be the intersection of forwa...
We prove the uniform hyperbolicity of the near-parabolic renormalization operators acting on an infi...
Holomorphic renormalization plays an important role in complex polynomial dynamics. We consider cert...
In this thesis we propose an arithmetic topological model for the post-critical set of infinitely qu...
We prove {\em a priori} bounds for Feigenbaum quadratic polynomials, i.e., infinitely renormalizable...
We study (Lebesgue) typical orbits of quadratic polynomials $P_a(z)=e^{2\pi a} z+z^2: C -> C$, with ...
The connectedness of the tongues of the double standard map family is shown by quasiconformal deform...
We gain tight rigorous bounds on the renormalisation fixed point for period doubling in families of ...
In this paper we describe the well studied process of renormalization of quadratic polynomials from ...
This thesis consists of an introduction and four research papers concerning dynamical systems, focus...
The pressure function p(t) of a non-recurrent map is real analytic on some interval (0,t_*) with t_*...
One of the main questions in the field of complex dynamics is the question whether the Mandelbrot se...
In this paper geometric properties of infinitely renormalizable real Henon-like maps F in R-2 are st...
Let f be a real rational function with all critical points on the extended real axis and of even ord...
Since its inception in the 1970s at the hands of Feigenbaum and, independently, Coullet and Tresser ...
Let f be an infinitely-renormalizable quadratic polynomial and J_\infty be the intersection of forwa...
We prove the uniform hyperbolicity of the near-parabolic renormalization operators acting on an infi...
Holomorphic renormalization plays an important role in complex polynomial dynamics. We consider cert...
In this thesis we propose an arithmetic topological model for the post-critical set of infinitely qu...
We prove {\em a priori} bounds for Feigenbaum quadratic polynomials, i.e., infinitely renormalizable...
We study (Lebesgue) typical orbits of quadratic polynomials $P_a(z)=e^{2\pi a} z+z^2: C -> C$, with ...
The connectedness of the tongues of the double standard map family is shown by quasiconformal deform...
We gain tight rigorous bounds on the renormalisation fixed point for period doubling in families of ...
In this paper we describe the well studied process of renormalization of quadratic polynomials from ...
This thesis consists of an introduction and four research papers concerning dynamical systems, focus...
The pressure function p(t) of a non-recurrent map is real analytic on some interval (0,t_*) with t_*...
One of the main questions in the field of complex dynamics is the question whether the Mandelbrot se...
In this paper geometric properties of infinitely renormalizable real Henon-like maps F in R-2 are st...
Let f be a real rational function with all critical points on the extended real axis and of even ord...
Since its inception in the 1970s at the hands of Feigenbaum and, independently, Coullet and Tresser ...