scholarly journals Fractal dimensions for Jarník limit sets of geometrically finite Kleinian groups; the semi-classical approach

1995 ◽  
Vol 33 (2) ◽  
pp. 385-403 ◽  
Author(s):  
Bernd Stratmann
Keyword(s):  
Fractal Dimensions ◽  
Kleinian Groups ◽  
Classical Approach ◽  
Limit Sets ◽  
Geometrically Finite

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 geometrically finite free Kleinian groups

1984 ◽  
Vol 36 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Tohru Akaza ◽  
Katsumi Inoue
Keyword(s):  
Kleinian Groups ◽  
Limit Sets ◽  
Geometrically Finite

scholarly journals Rigidity of limit sets for nonplanar geometrically finite Kleinian groups of the second kind

2015 ◽  
Vol 178 (1) ◽  
pp. 95-101
Author(s):  
Lior Fishman ◽  
David Simmons ◽  
Mariusz Urbański
Keyword(s):  
Kleinian Groups ◽  
Limit Sets ◽  
Geometrically Finite

Discrete Lyapunov exponents and Hausdorff dimension

2000 ◽  
Vol 20 (1) ◽  
pp. 145-172 ◽  
Author(s):  
SHMUEL FRIEDLAND
Keyword(s):  
Hausdorff Dimension ◽  
Finite Type ◽  
Lyapunov Exponents ◽  
Thermodynamic Formalism ◽  
Sufficient Conditions ◽  
Kleinian Groups ◽  
Limit Sets ◽  
Geometrically Finite ◽  
Subshifts Of Finite Type ◽  
Discrete Analogs

We study certain metrics on subshifts of finite type for which we define the discrete analogs of Lyapunov exponents. We prove Young's formula for $\mu$-Hausdorff dimension. We give sufficient conditions on the above metrics for which the Hausdorff dimension is given by thermodynamic formalism. We apply these results to the Hausdorff dimension of the limit sets of geometrically finite, purely loxodromic, Kleinian groups.

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.

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