scholarly journals Hereditarily non uniformly perfect non-autonomous Julia sets

2020 ◽  
Vol 40 (1) ◽  
pp. 33-46
Author(s):  
Mark Comerford ◽  
◽  
Rich Stankewitz ◽  
Hiroki Sumi ◽  
◽  
...  
Keyword(s):  
Julia Sets ◽  
Uniformly Perfect

scholarly journals Julia sets of uniformly quasiregular mappings are uniformly perfect

2011 ◽  
Vol 151 (3) ◽  
pp. 541-550 ◽  
Author(s):  
ALASTAIR N. FLETCHER ◽  
DANIEL A. NICKS
Keyword(s):  
Hausdorff Dimension ◽  
Analogous Result ◽  
Julia Set ◽  
Julia Sets ◽  
Quasiregular Mapping ◽  
Higher Dimensions ◽  
Ring Domain ◽  
Rational Map ◽  
Quasiregular Mappings ◽  
Uniformly Perfect

AbstractIt is well known that the Julia set J(f) of a rational map f: ℂ → ℂ is uniformly perfect; that is, every ring domain which separates J(f) has bounded modulus, with the bound depending only on f. In this paper we prove that an analogous result is true in higher dimensions; namely, that the Julia set J(f) of a uniformly quasiregular mapping f: ℝn → ℝn is uniformly perfect. In particular, this implies that the Julia set of a uniformly quasiregular mapping has positive Hausdorff dimension.

scholarly journals Julia Sets are Uniformly Perfect

1992 ◽  
Vol 116 (1) ◽  
pp. 251 ◽  
Author(s):  
R. Mane ◽  
L. F. Da Rocha
Keyword(s):  
Julia Sets ◽  
Uniformly Perfect

scholarly journals Uniformly perfect Julia sets of meromorphic functions

2005 ◽  
Vol 71 (3) ◽  
pp. 387-397
Author(s):  
Sheng Wang ◽  
Liang-Wen Liao
Keyword(s):  
Meromorphic Functions ◽  
Julia Sets ◽  
Rational Functions ◽  
Skew Product ◽  
Finitely Generated ◽  
Uniformly Perfect

Julia sets of meromorphic functions are uniformly perfect under some suitable conditions. So are Julia sets of the skew product associated with finitely generated semigroup of rational functions.

scholarly journals Julia sets are uniformly perfect

1992 ◽  
Vol 116 (1) ◽  
pp. 251-251 ◽  
Author(s):  
R. Ma{ñ{é ◽  
L. F. da Rocha
Keyword(s):  
Julia Sets ◽  
Uniformly Perfect

Julia sets of rational functions are uniformly perfect

1993 ◽  
Vol 113 (3) ◽  
pp. 543-559 ◽  
Author(s):  
A. Hinkkanen
Keyword(s):  
Rational Function ◽  
Julia Set ◽  
Julia Sets ◽  
Rational Functions ◽  
Uniformly Perfect

AbstractLetfbe a rational function of degree at least two. We shall prove that the Julia setJ(f) offis uniformly perfect. This means that there is a constantc∈(0, 1) depending onfonly such that wheneverz∈J(f) and 0 <r< diamJ(f) thenJ(f) intersects the annulus.

scholarly journals Uniform perfectness of the Berkovich Julia sets in non-archimedean dynamics

2021 ◽  
pp. 1-18
Author(s):  
YÛSUKE OKUYAMA
Keyword(s):  
Rational Function ◽  
Julia Set ◽  
Julia Sets ◽  
Projective Line ◽  
Closed Field ◽  
Fatou Component ◽  
Algebraically Closed Field ◽  
Absolute Value ◽  
Uniformly Perfect ◽  
Uniform Perfectness

Abstract We show that a rational function f of degree $>1$ on the projective line over an algebraically closed field that is complete with respect to a non-trivial and non-archimedean absolute value has no potentially good reductions if and only if the Berkovich Julia set of f is uniformly perfect. As an application, a uniform regularity of the boundary of each Berkovich Fatou component of f is also established.

FIXED POINTS-JULIA SETS

2020 ◽  
Vol 9 (9) ◽  
pp. 6759-6763
Author(s):  
G. Subathra ◽  
G. Jayalalitha
Keyword(s):  
Fixed Points ◽  
Julia Sets

Dynamics of a family of orbitally continuous mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3507-3517
Author(s):  
Abhijit Pant ◽  
R.P. Pant ◽  
Kuldeep Prakash
Keyword(s):  
Fixed Points ◽  
Julia Sets ◽  
Real Numbers ◽  
Continuous Mappings ◽  
Non Linear

The aim of the present paper is to study the dynamics of a class of orbitally continuous non-linear mappings defined on the set of real numbers and to apply the results on dynamics of functions to obtain tests of divisibility. We show that this class of mappings contains chaotic mappings. We also draw Julia sets of certain iterations related to multiple lowering mappings and employ the variations in the complexity of Julia sets to illustrate the results on the quotient and remainder. The notion of orbital continuity was introduced by Lj. B. Ciric and is an important tool in establishing existence of fixed points.

On uniformly perfect boundary of stable domains in iteration of meromorphic functions II

2002 ◽  
Vol 132 (3) ◽  
pp. 531-544 ◽  
Author(s):  
ZHENG JIAN-HUA
Keyword(s):  
Entire Function ◽  
Meromorphic Function ◽  
Meromorphic Functions ◽  
Julia Set ◽  
Fatou Set ◽  
Deficient Value ◽  
Uniformly Perfect ◽  
Simply Connected ◽  
Stable Domains ◽  
Uniform Perfectness

We investigate uniform perfectness of the Julia set of a transcendental meromorphic function with finitely many poles and prove that the Julia set of such a meromorphic function is not uniformly perfect if it has only bounded components. The Julia set of an entire function is uniformly perfect if and only if the Julia set including infinity is connected and every component of the Fatou set is simply connected. Furthermore if an entire function has a finite deficient value in the sense of Nevanlinna, then it has no multiply connected stable domains. Finally, we give some examples of meromorphic functions with uniformly perfect Julia sets.

Sign in / Sign up

Export Citation Format

Share Document