Add to ORKGAccording to the Thurston No Wandering Triangle Theorem, a branching point in a locally connected quadratic Julia set is either preperiodic or precritical. Blokh and Oversteegen proved that this theorem does not hold for higher degree Julia sets: there exist cubic polynomials whose Julia set is a locally connected dendrite with a branching point which is neither preperiodic nor precritical. In this article, we reprove this result, constructing such cubic polynomials as limits of cubic polynomials for which one critical point eventually maps to the other critical point which eventually maps to a repelling fixed point
28 pages, 3 figures. The authors would like to thank the referee for his thorough reading of the man...
Let 0 < θ < 1 be an irrational number with continued fraction expansion θ = [a1, a2, a3,...], ...
We prove that if the Julia set of a rational function is connected, and the trajectories of its crit...
21 pages, 13 figuresInternational audienceAccording to the Thurston No Wandering Triangle Theorem, a...
We consider non-autonomous iteration which is a generalization of standard polynomial iteration wher...
Local connectivity of Julia sets for unicritical polynomials By JEREMY KAHN and MIKHAIL LYUBICH We p...
In the dynamics of quadratic polynomials Pc(z) = z2 + c in the complex plan, Yoccoz has proved that...
This paper deals with Julia sets of polynomials and, more general, functions meromorphic on the comp...
AbstractLet P be a polynomial with a connected Julia set J. We use continuum theory to show that it ...
In this paper we shall consider real polynomials with one (possibly degenerate) non-escaping critica...
The Mandelbrot set of the quadratic polynomial pc(z)=z^2+c is the set of those values c such that th...
For polynomials, local connectivity of Julia sets is a much-studied and important property. Indeed, ...
There is a neat dichotomy for the Julia sets of quadratic rational maps; that is, they are either co...
In this paper we present the alternated Julia sets, obtained by alternated iteration of two maps of ...
It is known that the disconnected Julia set of any polynomial map does not contain buried Julia comp...
28 pages, 3 figures. The authors would like to thank the referee for his thorough reading of the man...
Let 0 < θ < 1 be an irrational number with continued fraction expansion θ = [a1, a2, a3,...], ...
We prove that if the Julia set of a rational function is connected, and the trajectories of its crit...
21 pages, 13 figuresInternational audienceAccording to the Thurston No Wandering Triangle Theorem, a...
We consider non-autonomous iteration which is a generalization of standard polynomial iteration wher...
Local connectivity of Julia sets for unicritical polynomials By JEREMY KAHN and MIKHAIL LYUBICH We p...
In the dynamics of quadratic polynomials Pc(z) = z2 + c in the complex plan, Yoccoz has proved that...
This paper deals with Julia sets of polynomials and, more general, functions meromorphic on the comp...
AbstractLet P be a polynomial with a connected Julia set J. We use continuum theory to show that it ...
In this paper we shall consider real polynomials with one (possibly degenerate) non-escaping critica...
The Mandelbrot set of the quadratic polynomial pc(z)=z^2+c is the set of those values c such that th...
For polynomials, local connectivity of Julia sets is a much-studied and important property. Indeed, ...
There is a neat dichotomy for the Julia sets of quadratic rational maps; that is, they are either co...
In this paper we present the alternated Julia sets, obtained by alternated iteration of two maps of ...
It is known that the disconnected Julia set of any polynomial map does not contain buried Julia comp...
28 pages, 3 figures. The authors would like to thank the referee for his thorough reading of the man...
Let 0 < θ < 1 be an irrational number with continued fraction expansion θ = [a1, a2, a3,...], ...
We prove that if the Julia set of a rational function is connected, and the trajectories of its crit...