This paper is based on the author’s previous work [S4]. We consider fiber-preserving complex dynamics on fiber bundles whose fibers are Riemann spheres and whose base spaces are compact metric spaces. In this context, without any assumption on (semi-)hyperbolicity, we show that the fiberwise Julia sets are uniformly perfect. From this result, we show that, for any semigroup G generated by a com...

We consider complex polynomials f (z) = z ℓ + c1 for ℓ ∈ 2N and c1 ∈ R, and find some combinatorial types and values of ℓ such that there is no invariant probability measure equivalent to conformal measure on the Julia set. This holds for particular Fibonacci-like and Feigenbaum combinatorial types when ℓ sufficiently large and also for a class of 'long–branched' maps of any critical order.

Instead of intertextuality, can one perhaps speak of an intervisuality? As a way of understanding how the meaning of images are shaped by other images related to or existing around them? As for intervisuality, I’m drawing on notions of intertextuality as introduced by Julia Kristeva[1]. Kristeva referred to texts in terms of two axes: a horizontal axis connecting the author and reader of a text...

To study nite Borel measures on the Riemann sphere invariant under a rational function R of degree greater than one, we decompose them in an R-invariant component measure supported on the Julia set and a nite number of mutually singular R-invariant component measures vanishing on the Julia set. The latter ones can be described easily. For a characterization of the former one, we use a general a...

We estimate the upper box and Hausdorff dimensions of the Julia set of an expanding semigroup generated by finitely many rational functions, using the thermodynamic formalism in ergodic theory. Furthermore, we show Bowen’s formula, and the existence and uniqueness of a conformal measure, for a finitely generated expanding semigroup satisfying the open set condition.

We prove that a nonempty, proper subset S of the complex plane can be approximated in a strong sense by polynomial filled Julia sets if and only if S is bounded and Ĉ \ int(S) is connected. The proof that such a set is approximable by filled Julia sets is constructive and relies on Fekete polynomials. Illustrative examples are presented. We also prove an estimate for the rate of approximation i...

We define a locally Sierpinski Julia set to be a Julia set of an elliptic function which is a Sierpinski curve in each fundamental domain for the lattice. In order to construct examples, we give sufficient conditions on a lattice for which the corresponding Weierstrass elliptic ℘ function is locally connected and quadratic-like, and we use these results to prove the existence of locally Sierpin...

Socially desirable responding and sexuality self‐reports Cindy M. Meston , Julia R. Heiman , Paul D. Trapnell & Delroy L. Paulhus To cite this article: Cindy M. Meston , Julia R. Heiman , Paul D. Trapnell & Delroy L. Paulhus (1998) Socially desirable responding and sexuality self‐reports, The Journal of Sex Research, 35:2, 148-157, DOI: 10.1080/00224499809551928 To link to this article: http://...

A locally connected quadratic Siegel Julia set has a simple explicit topological model. Such a set is computable if there exists an algorithm to draw it on a computer screen with an arbitrary resolution. We constructively produce parameter values for Siegel quadratics for which the Julia sets are non-computable, yet locally connected.

In this paper we investigate the support of the unique measure of maximal entropy of complex Hénon maps, J∗. The main question is whether this set is the same as the analogue of the Julia set J .