It is known that the disconnected Julia set of any polynomial map does not contain buried Julia components. But such Julia components may arise for rational maps. The first example is due to Curtis T. McMullen who provided a family of rational maps for which the Julia sets are Cantor of Jordan curves. However all known examples of buried Julia components, up to now, are points or Jordan curves and comes from rational maps of degree at least 5. This paper introduce a family of hyperbolic rational maps with disconnected Julia set whose exchanging dynamics of postcritically separating Julia components is encoded by a weighted dynamical tree. Each of these Julia sets presents buried Julia components of several types: points, Jordan curves, but ...
It is known that for a rational map ƒ with a disconnected Julia set, the set of wandering Julia comp...
AbstractLet f:C^→C^ be a subhyperbolic rational map of degree d. We construct a set of “proper” codi...
28 pages, 3 figures. The authors would like to thank the referee for his thorough reading of the man...
We give a topological characterization of rational maps with disconnected Julia sets. Our results ex...
There is a neat dichotomy for the Julia sets of quadratic rational maps; that is, they are either co...
There is a neat dichotomy for the Julia sets of quadratic rational maps; that is, they are either co...
Abstract. Any Jordan curve in the complex plane can be approxi-mated arbitrarily well in the Hausdor...
Abstract. We study the geometric properties of the Julia sets of McMullen maps fλ(z) = zm +λ/zl, whe...
In this thesis we study the topological properties of the Julia sets generated by iterating a single...
We introduce a generalization of the McMullen family fλ(z) = zn + λ/zd. In 1988 C. McMullen showed ...
In this thesis we investigate degeneration of rational maps and generation of parabolic cycles. Ther...
Abstract. In this paper we prove the existence of a new type of Sierpinski curve Julia set for certa...
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 20...
For the family of complex rational maps F_λ(z)=z^n+λ/z^d, where λ is a complex parameter and n, d ≥ ...
International audienceWe show that the Fatou components of a semi-hyperbolic rational map are John d...
It is known that for a rational map ƒ with a disconnected Julia set, the set of wandering Julia comp...
AbstractLet f:C^→C^ be a subhyperbolic rational map of degree d. We construct a set of “proper” codi...
28 pages, 3 figures. The authors would like to thank the referee for his thorough reading of the man...
We give a topological characterization of rational maps with disconnected Julia sets. Our results ex...
There is a neat dichotomy for the Julia sets of quadratic rational maps; that is, they are either co...
There is a neat dichotomy for the Julia sets of quadratic rational maps; that is, they are either co...
Abstract. Any Jordan curve in the complex plane can be approxi-mated arbitrarily well in the Hausdor...
Abstract. We study the geometric properties of the Julia sets of McMullen maps fλ(z) = zm +λ/zl, whe...
In this thesis we study the topological properties of the Julia sets generated by iterating a single...
We introduce a generalization of the McMullen family fλ(z) = zn + λ/zd. In 1988 C. McMullen showed ...
In this thesis we investigate degeneration of rational maps and generation of parabolic cycles. Ther...
Abstract. In this paper we prove the existence of a new type of Sierpinski curve Julia set for certa...
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 20...
For the family of complex rational maps F_λ(z)=z^n+λ/z^d, where λ is a complex parameter and n, d ≥ ...
International audienceWe show that the Fatou components of a semi-hyperbolic rational map are John d...
It is known that for a rational map ƒ with a disconnected Julia set, the set of wandering Julia comp...
AbstractLet f:C^→C^ be a subhyperbolic rational map of degree d. We construct a set of “proper” codi...
28 pages, 3 figures. The authors would like to thank the referee for his thorough reading of the man...