Convergence and Möbius Groups

1988 ◽  
pp. 113-140 ◽  
Author(s):  
Gaven J. Martin ◽  
Pekka Tukia
Keyword(s):  
Möbius Groups

scholarly journals The limit map of a homomorphism of discrete Möbius groups

1995 ◽  
Vol 82 (1) ◽  
pp. 97-132 ◽  
Author(s):  
Pekka Tukia
Keyword(s):  
Möbius Groups

scholarly journals Examples of Möbius-like groups which are not Möbius groups

1999 ◽  
Vol 351 (12) ◽  
pp. 4823-4835 ◽  
Author(s):  
Nataša Kovačević
Keyword(s):  
Möbius Groups

Complex dynamics of Möbius semigroups

2012 ◽  
Vol 32 (6) ◽  
pp. 1889-1929 ◽  
Author(s):  
DAVID FRIED ◽  
SEBASTIAN M. MAROTTA ◽  
RICH STANKEWITZ
Keyword(s):  
Complex Dynamics ◽  
Riemann Sphere ◽  
Julia Sets ◽  
Fibonacci Sequence ◽  
Rational Functions ◽  
Möbius Transformations ◽  
Random Dynamics ◽  
Compare And Contrast ◽  
Möbius Groups ◽  
Mobius Transformations

AbstractWe study the dynamics of semigroups of Möbius transformations on the Riemann sphere, especially their Julia sets and attractors. This theory relates to the dynamics of rational functions, rational semigroups, and Möbius groups and we compare and contrast these theories. We particularly examine Caruso’s family of Möbius semigroups, based on a random dynamics variant of the Fibonacci sequence.

KLEINIAN GROUPS WITH REAL PARAMETERS

2001 ◽  
Vol 03 (02) ◽  
pp. 163-186 ◽  
Author(s):  
F. W. GEHRING ◽  
J. P. GILMAN ◽  
G. J. MARTIN
Keyword(s):  
General Structure ◽  
Kleinian Groups ◽  
Analytic Space ◽  
Fuchsian Groups ◽  
Discrete Groups ◽  
Möbius Groups

We find all real points of the analytic space of two generator Möbius groups with one generator elliptic of order two. Geometrically this is a certain slice through the space of two generator discrete groups, analogous to the Riley slice, though of a very different nature. We obtain applications concerning the general structure of the space of all two generator Kleinian groups and various universal constraints for Fuchsian groups.

scholarly journals Axial distances in discrete Mobius groups.

1992 ◽  
Vol 89 (6) ◽  
pp. 1999-2001 ◽  
Author(s):  
F. W. Gehring ◽  
G. J. Martin
Keyword(s):  
Möbius Groups
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