Iterated function systems (if ss) are introduced as a unified way of generating a broad class
of fractals. These fractals are often attractors for if ss and occur as the supports of probability …

If one perturbs the analytic dynamical system zz on the Riemann sphere C to z-4 z2+ az for
small a, the following happens: Before perturbation the round unit circle C is invariant under …

4. The consequences of Montel's Theorem 5. The Julia set is the closure of the set of
repelling periodic points 6. Classical results concerning the Fatou set 7. Sullivan's …

Recently there has been a great deal of interest in the theory of orthogonal polynomials. The
number of books treating the subject, however, is limited. This monograph brings together …

The basic theory and properties of Iterated Function Systems are given, comparing the
original approaches of Hutchinson [47] and Barnsley and Demko [8]. Some examples and …

1 Introduction Page 1 ASYMPTOTICS OF CHEBYSHEV POLYNOMIALS. IV. COMMENTS ON
THE COMPLEX CASE By JACOB S. CHRISTIANSEN ∗ , BARRY SIMON † AND MAXIM …

The inverse problem for several classes of fractals in one and two dimensions can be
profitably solved via the application of the classical theory of moments. This new perspective …

We introduce the Mellin transform of the balanced invariant measure associated to the Julia
set generated by a rational transformation. We show that its analytic continuation is a …

Résumé Le recouvrement par des arcs disposés au hasard, les cascades self-similaires de
Benoît Mandelbrot, et le chaos multiplicatif sont des cas particuliers d'une théorie générale …

Let ℐ be the Jacobi matrix associated with polynomial T (z) of degree N≧ 2. The spectrum of
ℐ is the Julia set associated with T (z) which in many cases is a Cantor set. Let ℐ (1) denote …