Filled Julia Sets of Chebyshev Polynomials

被引：2

作者：

Christiansen, Jacob Stordal ^{[1
]}

Henriksen, Christian ^{[2
]}

Pedersen, Henrik Laurberg ^{[3
]}

Petersen, Carsten Lunde ^{[4
]}

机构：

[1] Lund Univ, Ctr Math Sci, Box 118, S-22100 Lund, Sweden

[2] Tech Univ Denmark, DTU Compute, Build 303B, DK-2800 Lyngby, Denmark

[3] Univ Copenhagen, Dept Math Sci, Univ Pk 5, DK-2100 Copenhagen, Denmark

[4] Roskilde Univ, Dept Sci & Environm, DK-4000 Roskilde, Denmark

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2021年 / 31卷 / 12期

关键词：

Chebyshev polynomials; Julia set; Green's function;

D O I：

10.1007/s12220-021-00716-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the possible Hausdorff limits of the Julia sets and filled Julia sets of subsequences of the sequence of dual Chebyshev polynomials of a non-polar compact set K subset of C and compare such limits to K. Moreover, we prove that the measures of maximal entropy for the sequence of dual Chebyshev polynomials of K converges weak* to the equilibrium measure on K.

引用

页码：12250 / 12263

页数：14

共 50 条

[31] The Julia sets of Chebyshev's method with small degrees
Nayak, Tarakanta
Pal, Soumen
NONLINEAR DYNAMICS, 2022, 110 (01) : 803 - 819
[32] Indecomposable continua and the Julia sets of polynomials, II
Childers, DK
Mayer, JC
Rogers, JT
TOPOLOGY AND ITS APPLICATIONS, 2006, 153 (10) : 1593 - 1602
[33] Local connectivity of Julia sets for unicritical polynomials
Kahn, Jeremy
Lyubich, Mikhail
ANNALS OF MATHEMATICS, 2009, 170 (01) : 413 - 426
[34] The topology of Julia sets for geometrically finite polynomials
Yin, YC
CHINESE ANNALS OF MATHEMATICS SERIES B, 1998, 19 (01) : 77 - 80
[35] THE TOPOLOGY OF JULIA SETS FOR GEOMETRICALLY FINITE POLYNOMIALS
Y IN Y ONGCHENG *
ChineseAnnalsofMathematics, 1998, (01) : 77 - 80
[36] HAUSDORFF DIMENSION OF JULIA SETS OF QUADRATIC POLYNOMIALS
Manuel Martinez, Luis
Ble, Gamaliel
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2018, 26 (03)
[37] Polynomials with Same Degree and Congruent Julia Sets
王仙桃
数学进展, 1998, (04) : 80 - 81
[38] Filled Julia sets with empty interior are computable
Binder, I.
Braverman, M.
Yampolsky, M.
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2007, 7 (04) : 405 - 416
[39] Filled Julia Sets with Empty Interior Are Computable
I. Binder
M. Braverman
M. Yampolsky
Foundations of Computational Mathematics, 2007, 7 : 405 - 416
[40] LS condition for filled Julia sets in C
Protin, Frederic
ANNALI DI MATEMATICA PURA ED APPLICATA, 2018, 197 (06) : 1845 - 1854

← 1 2 3 4 5 →