Lyapunov spectrum for rational maps (2008)
Gelfert, Katrin, Przytycki, Feliks, Rams, Michal
We study the dimension spectrum of Lyapunov exponents for rational maps on the Riemann sphere.
Nice inducing schemes and the thermodynamics of rational maps (2008)
Przytycki, Feliks, Rivera-Letelier, Juan
We consider the thermodynamic formalism of a complex rational map $f$ of degree at least two, viewed as a dynamical system acting on the Riemann sphere. More precisely, for a real parameter $t$ we...
Rigidity of Conformal Iterated Function Systems (2007)
Best Regards Mariusz, R. Daniel Mauldin, Feliks Przytycki, Mariusz Urba Nski
Abstract. The paper extends the rigidity of mixing expanding repellers theorem by D. Sullivan announced at 1986 IMC [Su], see also the unpublished manuscript by the second author [Pr]. We show that...
Rigidity Of, Feliks Przytycki, Mariusz Urba Nski
. We introduce and establish some basic properties of the tame rational functions. The class of these functions contains all the rational functions with no recurrent critical points in their Julia...
Statistical properties of topological Collet-Eckmann maps (2006)
Przytycki, Feliks, Rivera-Letelier, Juan
We study geometric and statistical properties of complex rational maps satisfying the Topological Collet-Eckmann Condition. We show that every such a rational map possesses a unique conformal...
On Hausdorff dimension of some Cantor attractors (2003)
Levin, Genadi, Przytycki, Feliks
We study what happens with the dimension of Feigenbaum-like attractors of smooth unimodal maps as the order of the critical point grows
Rigidity of Conformal Iterated Function (1999)
R. Daniel Mauldin, Feliks Przytycki, Mariusz Urbanski, Mariusz Urba Nski
. The paper extends the rigidity of mixing expanding repellers theorem by D. Sullivan announced at 1986 IMC [Su], see also the unpublished manuscript by the second author [Pr]. We show that for a...
Rigidity Of Tame Rational Functions (1998)
Feliks Przytycki, Mariusz Urbanski, Mariusz Urba Nski, Instytut Matematyczny Pan
We introduce and establish some basic properties of the tame rational functions. The class of these functions contains all the rational functions with no recurrent critical points in their Julia...
Conical limit set and Poincaré exponent for iterations of rational functions (1998)
. We contribute to the dictionary between action of Kleinian groups and iteration of rational functions on the Riemann sphere. We define the Poincar'e exponent ffi(f; z) = inffff 0 : P(z; ff) 0g...
Porosity Of Collet-Eckmann Julia Sets (1998)
Feliks Przytycki, Steffen Rohde
. We prove that the Julia set of a rational map of the Riemann sphere satisfying the Collet-Eckmann condition and having no parabolic periodic point is mean porous, if it is not the whole sphere. It...
Rigidity of Holomorphic Collet-Eckmann Repellers (1997)
Feliks Przytycki, Steffen Rohde
. We prove rigidity results for a class of non-uniformly hyperbolic holomorphic maps: If a holomorphic Collet-Eckmann map f is topologically conjugate to a holomorphic map g, then the conjugacy can...
Porosity of Collet-Eckmann Julia sets (1996)
Przytycki, Feliks, Rohde, Steffen
We prove that the Julia set of a rational map of the Riemann sphere satisfying the Collet-Eckmann condition and having no parabolic periodic point is mean porous, if it is not the whole sphere. It...
. --- We prove that for every polynomial f if its basin of attraction to 1 is Holder and Julia set contains only one critical point c then f is Collet-Eckmann, namely there exists ? 1; C ? 0 such...
On the transfer operator for rational functions on the Riemann sphere (1996)
Manfred Denker, Feliks Przytycki, Mariusz Urbanski, Mariusz Urba Nski
: Let T be a rational function of degree 2 on the Riemann sphere. Denote L OE the transfer operator of a Holder-continuous function OE on its Julia set J = J(T ) satisfying P (T; OE) ? sup z2J OE(z)....
On measure and Hausdorff dimension of Julia sets for holomorphic Collet--Eckmann maps (1995)
Let $f:\bar\bold C\to\bar\bold C$ be a rational map on the Riemann sphere , such that for every $f$-critical point $c\in J$ which forward trajectory does not contain any other critical point,...
On Measure And Hausdorff Dimension Of Julia Sets For Holomorphic Collet-Eckmann Maps (1995)
. Let f : C ! C be a rational map on the Riemann sphere , such that for every f-critical point c 2 J which forward trajectory does not contain any other critical point, j(f n ) 0 (f(c))j grows...
Iterations of rational functions: which hyperbolic components contain polynomials? (1994)
Let $H^d$ be the set of all rational maps of degree $d\ge 2$ on the Riemann sphere which are expanding on Julia set. We prove that if $f\in H^d$ and all or all but one critical points (or values) are...
Przytycki, Feliks, Zdunik, Anna
We prove that if A is the basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, then periodic points in the boundary of A are dense in...
We prove that if A is the basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, if $A$ is completely invariant (i.e. $f^{-1}(A)=A$),...
Problems in holomorphic dynamics (1992)
Bielefeld, Ben, Lyubich, Mikhail, Carleson, Lennart, Devaney, Robert, Eremenko, Alexandre, McMullen, Curt, ...
Contents: 1. Quasiconformal Surgery and Deformations: Ben Bielefeld, Questions in quasiconformal surgery; Curt McMullen, Rational maps and Teichm\"uller space; John Milnor, Thurston's algorithm...
Cantor sets in the line: scaling function and the smoothness of the shift map (1992)
Przytycki, Feliks, Tangerman, Folkert
Consider $d$ disjoint closed subintervals of the unit interval and consider an orientation preserving expanding map which maps each of these subintervals to the whole unit interval. The set of points...