# The box-counting dimension for geometrically finite Kleinian groups

B. Stratmann; Mariusz Urbański

Fundamenta Mathematicae (1996)

- Volume: 149, Issue: 1, page 83-93
- ISSN: 0016-2736

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topStratmann, B., and Urbański, Mariusz. "The box-counting dimension for geometrically finite Kleinian groups." Fundamenta Mathematicae 149.1 (1996): 83-93. <http://eudml.org/doc/212110>.

@article{Stratmann1996,

abstract = {We calculate the box-counting dimension of the limit set of a general geometrically finite Kleinian group. Using the 'global measure formula' for the Patterson measure and using an estimate on the horoball counting function we show that the Hausdorff dimension of the limit set is equal to both: the box-counting dimension and packing dimension of the limit set. Thus, by a result of Sullivan, we conclude that for a geometrically finite group these three different types of dimension coincide with the exponent of convergence of the group.},

author = {Stratmann, B., Urbański, Mariusz},

journal = {Fundamenta Mathematicae},

keywords = {limit sets; fractal dimensions; Patterson measure; finitely generated Fuchsian groups; exponent of convergence; Hausdorff dimension; box-counting dimension; geometrically finite Kleinian groups},

language = {eng},

number = {1},

pages = {83-93},

title = {The box-counting dimension for geometrically finite Kleinian groups},

url = {http://eudml.org/doc/212110},

volume = {149},

year = {1996},

}

TY - JOUR

AU - Stratmann, B.

AU - Urbański, Mariusz

TI - The box-counting dimension for geometrically finite Kleinian groups

JO - Fundamenta Mathematicae

PY - 1996

VL - 149

IS - 1

SP - 83

EP - 93

AB - We calculate the box-counting dimension of the limit set of a general geometrically finite Kleinian group. Using the 'global measure formula' for the Patterson measure and using an estimate on the horoball counting function we show that the Hausdorff dimension of the limit set is equal to both: the box-counting dimension and packing dimension of the limit set. Thus, by a result of Sullivan, we conclude that for a geometrically finite group these three different types of dimension coincide with the exponent of convergence of the group.

LA - eng

KW - limit sets; fractal dimensions; Patterson measure; finitely generated Fuchsian groups; exponent of convergence; Hausdorff dimension; box-counting dimension; geometrically finite Kleinian groups

UR - http://eudml.org/doc/212110

ER -

## References

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