Add to ORKGHyperbolic components, in a reasonable space of polynomial or rational maps, are well understood. But their topological boundaries can be very complicated. This talk will first describe a special case where the boundaries are very well behaved. It will then speculate about the other cases. Definitions. Let Ratn ⊂ P2n+1(C) be the space of all rational maps of degree n ≥ 2:( f (z) = ∑n 0 ajz j∑n 0 bjz
this article we survey a small constellation of such conjectures, centering around the density of hy...
Semihyperbolic rational maps of the Riemann sphere form a natural class of conformal dynamical syste...
Rational maps are self-maps of the Riemann sphere of the form z → p(z)/q(z) where p(z) and q(z) are ...
∗Revised version. The conjectures on page 16 were problematic, and have been corrected. The Problem ...
Abstract. Consider polynomial maps f: C → C of degree d ≥ 2, or more gen-erally polynomial maps from...
Let $R:\overline{\mathbb{C}}arrow\overline{\mathbb{C}} $ be a hyperbolic rational mapping. We assume...
We give a topological characterization of rational maps with disconnected Julia sets. Our results ex...
AbstractIn 1980's, Thurston established a combinatorial characterization for post-critically finite ...
Abstract. The tricorn is the connectedness locus of antiholomorphic quadratic polynomials. We invest...
Abstract. We describe an algorithm for distinguishing hyperbolic compo-nents in the parameter space ...
In this paper, we study hyperbolic rational maps with finitely connected Fatou sets. We construct mo...
In the moduli space of polynomial or rational maps of degree d, there exists a bifurcation measure w...
International audienceWe show that the Fatou components of a semi-hyperbolic rational map are John d...
It is known that the disconnected Julia set of any polynomial map does not contain buried Julia comp...
International audienceThe goal of this chapter is to explain some connections between hyperbolicity ...
this article we survey a small constellation of such conjectures, centering around the density of hy...
Semihyperbolic rational maps of the Riemann sphere form a natural class of conformal dynamical syste...
Rational maps are self-maps of the Riemann sphere of the form z → p(z)/q(z) where p(z) and q(z) are ...
∗Revised version. The conjectures on page 16 were problematic, and have been corrected. The Problem ...
Abstract. Consider polynomial maps f: C → C of degree d ≥ 2, or more gen-erally polynomial maps from...
Let $R:\overline{\mathbb{C}}arrow\overline{\mathbb{C}} $ be a hyperbolic rational mapping. We assume...
We give a topological characterization of rational maps with disconnected Julia sets. Our results ex...
AbstractIn 1980's, Thurston established a combinatorial characterization for post-critically finite ...
Abstract. The tricorn is the connectedness locus of antiholomorphic quadratic polynomials. We invest...
Abstract. We describe an algorithm for distinguishing hyperbolic compo-nents in the parameter space ...
In this paper, we study hyperbolic rational maps with finitely connected Fatou sets. We construct mo...
In the moduli space of polynomial or rational maps of degree d, there exists a bifurcation measure w...
International audienceWe show that the Fatou components of a semi-hyperbolic rational map are John d...
It is known that the disconnected Julia set of any polynomial map does not contain buried Julia comp...
International audienceThe goal of this chapter is to explain some connections between hyperbolicity ...
this article we survey a small constellation of such conjectures, centering around the density of hy...
Semihyperbolic rational maps of the Riemann sphere form a natural class of conformal dynamical syste...
Rational maps are self-maps of the Riemann sphere of the form z → p(z)/q(z) where p(z) and q(z) are ...