Constructing Locally Connected Non-Computable Julia Sets
نویسندگان
چکیده
منابع مشابه
Constructing Locally Connected Non-computable Julia Sets
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.
متن کاملNon-computable Julia sets
Polynomial Julia sets have emerged as the most studied examples of fractal sets generated by a dynamical system. Apart from the beautiful mathematics, one of the reasons for their popularity is the beauty of the computer-generated images of such sets. The algorithms used to draw these pictures vary; the most näıve work by iterating the center of a pixel to determine if it lies in the Julia set....
متن کاملBiaccessibility in Quadratic Julia Sets I: the Locally-connected Case
Let f : z 7→ z + c be a quadratic polynomial whose Julia set J is locallyconnected. We prove that the Brolin measure of the set of biaccessible points in J is zero except when f(z) = z − 2 is the Chebyshev quadratic polynomial for which the corresponding measure is one. §
متن کاملSome Rational Maps Whose Julia Sets Are Not Locally Connected
We describe examples of rational maps which are not topologically conjugate to a polynomial and whose Julia sets are connected but not locally connected. Introduction and motivations The dynamics of a rational map f acting on Ĉ is concentrated on its Julia set which is (by definition) the minimal compact set invariant by f and f−1 containing at least three points. The question of local connecti...
متن کاملBackward Stability for Polynomial Maps with Locally Connected Julia Sets
We study topological dynamics on unshielded planar continua with weak expanding properties at cycles for which we prove that the absence of wandering continua implies backward stability. Then we deduce from this that a polynomial f with a locally connected Julia set is backward stable outside any neighborhood of its attracting and neutral cycles. For a conformal measure μ this easily implies th...
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: Communications in Mathematical Physics
سال: 2009
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-009-0858-5