Iteration of Rational Functions.

1993 ◽  
Vol 100 (1) ◽  
pp. 90
Author(s):  
Robert L. Devaney ◽  
Alan F. Beardon
Keyword(s):  
Rational Functions ◽  
Iteration Of Rational Functions

Iteration of Rational Functions

1994 ◽  
Vol 78 (481) ◽  
pp. 101
Author(s):  
David Griffel ◽  
A. F. Beardon
Keyword(s):  
Rational Functions ◽  
Iteration Of Rational Functions

Iteration of Rational Functions (Alan F. Beardon)

SIAM Review ◽  
1993 ◽  
Vol 35 (2) ◽  
pp. 310-312
Author(s):  
Paul Blanchard
Keyword(s):  
Rational Functions ◽  
Iteration Of Rational Functions

On the iteration of rational functions

1978 ◽  
Vol 84 (3) ◽  
pp. 497-505 ◽  
Author(s):  
V. Garber
Keyword(s):  
Rational Function ◽  
Entire Functions ◽  
Rational Functions ◽  
Transcendental Entire Function ◽  
The Family ◽  
Transcendental Entire Functions ◽  
Definition Of ◽  
Iteration Of Rational Functions ◽  
Image Position ◽  
Set Of Points

In the theory of the iteration of a rational function or transcendental entire function R(z) of the complex variable z we study the sequence of natural iterates, {Rn(z):n = 0, 1,…}, of R, whereThe domain of definition of the iterates is , the extended complex plane (if R is rational), and (if R is entire transcendental) with the topology of the chordal metric and euclidean metric respectively. Fatou(5) and Julia(9) developed a global theory of the iteration of a rational function. In (6) Fatou extended the theory of (5) to transcendental entire functions. A central role is played in the theory by the F-set, F(R), of R, R rational or entire, which is defined to be the set of points at which the family of iterates do not form a normal family in the sense of Montel.

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