We explore the connected/disconnected dichotomy for the Julia set of polynomial automorphisms of C. We develop several aspects of the question, which was first studied by Bedford-Smillie [BS6, BS7]. We introduce a new sufficient condition for the connectivity of the Julia set, that carries over for certain Hénon-like and birational maps. We study the structure of disconnected Julia sets and the...

We investigate disfluency distribution rates within different moves from an interactive task-oriented experiment to further explore the suggestion by Bortfeld et al. [1] and Nicholson [2] that different types of disfluencies may fulfill varying functions. We focus on disfluency types within moves, or speech turns, where a speaker initiates something compared to a response to such a move. We fin...

In this paper we study the dynamics of regular polynomial automorphisms of C. These maps provide a natural generalization of complex Hénon maps in C to higher dimensions. For a given regular polynomial automorphism f we construct a filtration in C which has particular escape properties for the orbits of f . In the case when f is hyperbolic we obtain a complete description of its orbits. In the ...

We construct a transcendental entire function f with J(f) = C such that f has arbitrarily slow growth; that is, log |f(z)| ≤ φ(|z|) log |z| for |z| > r0, where φ is an arbitrary prescribed function tending to infinity. For an entire function f we denote the Julia set by J(f). By definition, it is the complement of the maximal open set F (f), the set of normality, where the iterates f form a nor...

We consider any transcendental meromorphic function f of Class S whose Julia set is a Jordan curve. We show that the Julia set of f either is an extended straight line or has Hausdorff dimension strictly greater than 1. The proof uses conformal iterated function systems and extends many earlier results of this type.

Let f be a non-constant and non-linear entire function, g an analytic self-map of C\{0}, and suppose that exp ◦f = g ◦ exp. It is shown that z is in the Julia set of f if and only if e is in the Julia set of g. 1991 Mathematics Subject Classification: 30D05, 58F23

We prove that the only possible biaccessible points in the Julia set of a Cremer quadratic polynomial are the Cremer fixed point and its preimages. This gives a partial answer to a question posed by C. McMullen on whether such a Julia set can contain any biaccessible point at all.