Open AccessSubhyperbolic Rational Maps with Identical Julia set
Author(s) -
Xia Sun,
Zhaoli Ma
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1903/1/012072
Subject(s) - julia set , permutable prime , converse , mathematics , class (philosophy) , set (abstract data type) , rational function , degree (music) , pure mathematics , computer science , geometry , artificial intelligence , physics , acoustics , programming language
Permutable rational functions have identical Julia set. However, is the converse right? We have found a class of rational functions with degree two, they have identical Julia set but are not permutable. Moreover, they have hyperbolic periodic points only.