Geometry, electrostatic measure and orthogonal polynomials on Julia sets for polynomials
نویسندگان
چکیده
منابع مشابه
Fekete Polynomials and Shapes of Julia Sets
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...
متن کاملSierpinski-curve Julia sets and singular perturbations of complex polynomials
In this paper we consider the family of rational maps of the complex plane given by z2 + λ z2 where λ is a complex parameter. We regard this family as a singular perturbation of the simple function z2. We show that, in any neighborhood of the origin in the parameter plane, there are infinitely many open sets of parameters for which the Julia sets of the correspondingmaps are Sierpinski curves. ...
متن کاملThe Julia Sets of Basic Unicremer Polynomials of Arbitrary Degree
Let P be a polynomial of degree d with a Cremer point p and no repelling or parabolic periodic bi-accessible points. We show that there are two types of such Julia sets JP . The red dwarf JP are nowhere connected im kleinen and such that the intersection of all impressions of external angles is a continuum containing p and the orbits of all critical images. The solar JP are such that every angl...
متن کاملComputation of connection coefficients and measure modifications for orthogonal polynomials
We observe that polynomial measure modifications for families of univariate orthogonal polynomials imply sparse connection coefficient relations. We therefore propose connecting L2 expansion coefficients between a polynomial family and a modified family by a sparse transformation. Accuracy and conditioning of the connection and its inverse are explored. The connection and recurrence coefficient...
متن کاملThe Solar Julia Sets of Basic Quadratic Cremer Polynomials
In general, little is known about the exact topological structure of Julia sets containing a Cremer point. In this paper we show that there exist quadratic Cremer Julia sets of positive area such that for a full Lebesgue measure set of angles the impressions are degenerate, the Julia set is connected im kleinen at the landing points of these rays, and these points are contained in no other impr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 1983
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385700002108