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Filled Julia Sets of Chebyshev Polynomials

Christiansen, Jacob Stordal LU ; Henriksen, Christian ; Pedersen, Henrik Laurberg and Petersen, Carsten Lunde (2021) In Journal of Geometric Analysis 31(12). p.12250-12263
Abstract

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⊂ 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.

Please use this url to cite or link to this publication:
author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Chebyshev polynomials, Green’s function, Julia set
in
Journal of Geometric Analysis
volume
31
issue
12
pages
12250 - 12263
publisher
Springer
external identifiers
  • scopus:85108343519
ISSN
1050-6926
DOI
10.1007/s12220-021-00716-y
language
English
LU publication?
yes
id
02d39a86-5453-4256-a6ff-29530bbcb525
date added to LUP
2021-07-16 13:14:12
date last changed
2022-04-27 02:53:00
@article{02d39a86-5453-4256-a6ff-29530bbcb525,
  abstract     = {{<p>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⊂ 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.</p>}},
  author       = {{Christiansen, Jacob Stordal and Henriksen, Christian and Pedersen, Henrik Laurberg and Petersen, Carsten Lunde}},
  issn         = {{1050-6926}},
  keywords     = {{Chebyshev polynomials; Green’s function; Julia set}},
  language     = {{eng}},
  number       = {{12}},
  pages        = {{12250--12263}},
  publisher    = {{Springer}},
  series       = {{Journal of Geometric Analysis}},
  title        = {{Filled Julia Sets of Chebyshev Polynomials}},
  url          = {{http://dx.doi.org/10.1007/s12220-021-00716-y}},
  doi          = {{10.1007/s12220-021-00716-y}},
  volume       = {{31}},
  year         = {{2021}},
}