Rational semigroups, random complex dynamics and singular functions on the complex plane

2010 ◽  
pp. 161-200 ◽  
Author(s):  
Hiroki Sumi
Keyword(s):  
Complex Plane ◽  
Complex Dynamics ◽  
Singular Functions ◽  
Random Complex

scholarly journals Structurally Similar Sets of Transcendental Entire Function

2018 ◽  
Vol 4 ◽  
pp. 11-16
Author(s):  
Bishnu Hari Subedi
Keyword(s):  
Entire Function ◽  
Complex Plane ◽  
Full Text ◽  
Complex Dynamics ◽  
Julia Set ◽  
Transcendental Entire Function ◽  
Fatou Set ◽  
Classical Sense

In complex dynamics, the complex plane is partitioned into invariant subsets. In classical sense, these subsets are of course Fatou set and Julia set. Rest of the abstract available with the full text

scholarly journals Random complex dynamics and devil's coliseums

Nonlinearity ◽  
2015 ◽  
Vol 28 (4) ◽  
pp. 1135-1161 ◽  
Author(s):  
Hiroki Sumi
Keyword(s):  
Complex Dynamics ◽  
Random Complex

scholarly journals On the Complex Dynamics of Continued and Discrete Cauchy’s Method

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Mohamed Lamine Sahari
Keyword(s):  
Complex Plane ◽  
Complex Dynamics ◽  
Initial Guess ◽  
Complex Polynomial ◽  
Fixed Degree ◽  
Cauchy's Method

Let p be a complex polynomial of fixed degree n. In this paper we show that Cauchy’s method may fail to find all zeros of p for any initial guess z0 lying in the complex plane and we propose several ways to find all zeros of a given polynomial using scaled Cauchy’s methods.

Frontiers in Complex Dynamics

2014 ◽  
Author(s):  
Araceli Bonifant ◽  
Misha Lyubich ◽  
Scott Sutherland
Keyword(s):  
Historical Perspective ◽  
Complex Dynamics ◽  
Short Paper ◽  
Combinatorial Group Theory ◽  
Entropy Theory ◽  
Holomorphic Dynamics ◽  
Eightieth Birthday ◽  
Several Variables ◽  
Fields Medal ◽  
Combinatorial Group

John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing.

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