Filled Julia sets with empty interior are computable

نویسندگان

  • Ilia Binder
  • Mark Braverman
  • Michael Yampolsky
چکیده

We show that if a polynomial filled Julia set has empty interior, then it is computable.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Pasting Together Julia Sets: A Worked Out Example of Mating

The operation of “mating” two suitable complex polynomial maps f1 and f2 constructs a new dynamical system by carefully pasting together the boundaries of their filled Julia sets so as to obtain a copy of the Riemann sphere, together with a rational map f1 ⊥⊥ f2 from this sphere to itself. This construction is particularly hard to visualize when the filled Julia sets K(fi) are dendrites, with n...

متن کامل

Computability of Julia Sets

In this paper we settle most of the open questions on algorithmic computability of Julia sets. In particular, we present an algorithm for constructing quadratics whose Julia sets are uncomputable. We also show that a filled Julia set of a polynomial is always computable.

متن کامل

Methods and Applications to Display Quaternion Julia Sets

After explaining the details of an efficient technique, developed in early 1980s, to plot digital images of quaternion filled-in Julia sets, later considerations on it will introduce a new modification for displaying such sets with no interior too. A step by step description via pseudo-C++ is given. The reader is assumed to be familiar with advanced programming and quaternion calculus.

متن کامل

Elementary Computable Topology

We revise and extend the foundation of computable topology in the framework of Type-2 theory of effectivity, TTE, where continuity and computability on finite and infinite sequences of symbols are defined canonically and transferred to abstract sets by means of notations and representations. We start from a computable topological space, which is a T0-space with a notation of a base such that in...

متن کامل

Parabolic Julia Sets are Polynomial Time Computable

In this paper we prove that parabolic Julia sets of rational functions are locally computable in polynomial time.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Foundations of Computational Mathematics

دوره 7  شماره 

صفحات  -

تاریخ انتشار 2007