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Julia Sets of Polynomials are Uniformly Perfect
Author(s) -
Hinkkanen A.
Publication year - 1994
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/26.2.153
Subject(s) - mathematics , julia set , annulus (botany) , combinatorics , degree (music) , polynomial , constant (computer programming) , discrete mathematics , mathematical analysis , physics , botany , computer science , acoustics , biology , programming language
Let f be a polynomial of degree at least two. We shall show that the Julia set J ( f ) of f is uniformly perfect. This means that there is a constant c ∈(0,1) depending on f only such that whenever z∈ J ( f ) and 0 < r < diam J ( f ) then J ( f ) intersects the annulus { w : cr ⩽ | w — z | ⩽ r }.