Filled Julia Sets of Chebyshev Polynomials
(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:
https://lup.lub.lu.se/record/02d39a86-5453-4256-a6ff-29530bbcb525
- author
- Christiansen, Jacob Stordal LU ; Henriksen, Christian ; Pedersen, Henrik Laurberg and Petersen, Carsten Lunde
- organization
- publishing date
- 2021
- 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}}, }