Introduction to papers on Kleinian groups, their fractal limit sets, and IFS: history, recollections, and acknowledgments

2004 ◽  
pp. 171-177
Author(s):  
Benoit B. Mandelbrot
Keyword(s):  
Kleinian Groups ◽  
Limit Sets

scholarly journals Free vs. locally free Kleinian groups

2019 ◽  
Vol 2019 (746) ◽  
pp. 149-170
Author(s):  
Pekka Pankka ◽  
Juan Souto
Keyword(s):  
Hausdorff Dimension ◽  
Kleinian Group ◽  
Cantor Set ◽  
Cantor Sets ◽  
Kleinian Groups ◽  
The Other ◽  
Limit Set ◽  
Limit Sets ◽  
Other Hand

Abstract We prove that Kleinian groups whose limit sets are Cantor sets of Hausdorff dimension < 1 are free. On the other hand we construct for any ε > 0 an example of a non-free purely hyperbolic Kleinian group whose limit set is a Cantor set of Hausdorff dimension < 1 + ε.

FOX-ARTIN ARC AND CONSTRUCTING KLEINIAN GROUPS ACTING ON S3 WITH LIMIT SET A WILD CANTOR SET

1995 ◽  
Vol 06 (01) ◽  
pp. 19-32 ◽  
Author(s):  
NIKOLAY GUSEVSKII ◽  
HELEN KLIMENKO
Keyword(s):  
Cantor Set ◽  
Cantor Sets ◽  
Kleinian Groups ◽  
Limit Set ◽  
Limit Sets ◽  
Geometrically Finite ◽  
Wild Cantor Set ◽  
Wild Cantor Sets

We construct purely loxodromic, geometrically finite, free Kleinian groups acting on S3 whose limit sets are wild Cantor sets. Our construction is closely related to the construction of the wild Fox–Artin arc.

scholarly journals Limit sets of some Kleinian groups

1975 ◽  
Vol 27 (1) ◽  
pp. 91-97
Author(s):  
Hiro-o Yamamoto
Keyword(s):  
Kleinian Groups ◽  
Limit Sets

scholarly journals The residual limit sets of Kleinian groups

1973 ◽  
Vol 130 (0) ◽  
pp. 127-144 ◽  
Author(s):  
William Abikoff
Keyword(s):  
Kleinian Groups ◽  
Limit Sets

Meromorphic multifunctions in complex dynamics

1992 ◽  
Vol 12 (1) ◽  
pp. 39-52 ◽  
Author(s):  
L. Baribeau ◽  
T. J. Ransford
Keyword(s):  
Critical Points ◽  
Complex Dynamics ◽  
Julia Set ◽  
Kleinian Groups ◽  
Rational Maps ◽  
Analytic Family ◽  
Limit Sets ◽  
Upper Semicontinuous ◽  
Open Set ◽  
Similar Vein

AbstractLet {RA} be an analytic family of rational maps and denote by j(λ) the Julia set of Rλ. We prove that the upper semicontinuous regularization j(λ) of j(λ) (which coincides with j(λ) for all λ in a dense open set) is a meromorphic multifunction, and give applications that illustrate the instability of Julia sets. In a similar vein, we also consider forward orbits of critical points and limit sets of Kleinian groups.

scholarly journals Wild knots in higher dimensions as limit sets of Kleinian groups

2009 ◽  
Vol 13 (11) ◽  
pp. 197-216 ◽  
Author(s):  
Margareta Boege ◽  
Gabriela Hinojosa ◽  
Alberto Verjovsky
Keyword(s):  
Higher Dimensions ◽  
Kleinian Groups ◽  
Limit Sets

On the local connectivity of limit sets of kleinian groups

1996 ◽  
Vol 31 (2) ◽  
pp. 177-183 ◽  
Author(s):  
James W. Anderson ◽  
Bernard Maskit
Keyword(s):  
Kleinian Groups ◽  
Local Connectivity ◽  
Limit Sets
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