COMPUTABILITY OF JULIA SETS

被引：11
作者：
Braverman, Mark [1 ]
Yampolsky, Michael [2 ]
机构：
[1] Univ Toronto, Dept Comp Sci, Toronto, ON M5S 3G4, Canada
[2] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada
来源：
MOSCOW MATHEMATICAL JOURNAL | 2008年 / 8卷 / 02期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Julia set; computability; complexity;
D O I：
10.17323/1609-4514-2008-8-2-185-231
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we settle most of the open questions on algorithmic computability of Julia sets. In particular, we present analgorithm for constructing quadratics whose Julia sets are uncomputable. We also show that a filled Julia set of a polynomial is always computable.
引用
收藏
页码：185 / 231
页数：47
相关论文
共 51 条
[1]  
Ahlfors L. V., 2006, U LECT SERIES, V38
[2]  
[Anonymous], 1993, Foundations of Computing Series
[3]  
[Anonymous], 1998, COMPLEXITY REAL COMP, DOI DOI 10.1007/978-1-4612-0701-6
[4]  
AVILA A, 2004, ACTA MATH, V193
[5]  
Banach S., 1937, ANN POLON MATH, V16
[6]   Filled Julia sets with empty interior are computable [J].
Binder, I. ;
Braverman, M. ;
Yampolsky, M. .
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2007, 7 (04) :405-416
[7]   On computational complexity of Siegel Julia sets [J].
Binder, I ;
Braverman, M ;
Yampolsky, M .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2006, 264 (02) :317-334
[8]  
Bishop E.A., 1985, GRUNDLEHREN MATH WIS, V279
[9]   Non-computable Julia sets [J].
Braverman, M. ;
Yampolsky, M. .
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 19 (03) :551-578
[10]  
BRAVERMAN M, 2006, NOTICES AMS, V53
123456