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Abstract
Given a nonempty bounded subset of hyperbolic space and a Kleinian group acting on that space, the orbital set
is the orbit of the given set under the action of the group. We may
view orbital sets as bounded (often fractal) subsets of Euclidean space.
We prove that the upper box dimension of an orbital set is given by the
maximum of three quantities: the upper box dimension of the given set,
the Poincaré exponent of the Kleinian group, and the upper box dimension
of the limit set of the Kleinian group. Since we do not make any
assumptions about the Kleinian group, none of the terms in the maximum
can be removed in general. We show by constructing an explicit example
that our assumption that the given set is bounded (in the hyperbolic
metric) cannot be removed in general.
Original language  English 

Pages (fromto)  267278 
Number of pages  12 
Journal  Journal of Fractal Geometry 
Volume  10 
Issue number  3/4 
Early online date  30 Aug 2023 
DOIs  
Publication status  Published  6 Oct 2023 
Keywords
 Orbital set
 Kleinian group
 Poincaré exponent
 Upper box dimension
 Limit set
 Inhomogeneous attractor
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Dive into the research topics of 'Dimensions of Kleinian orbital sets'. Together they form a unique fingerprint.Projects
 2 Finished

New perspectives in the dimension: New perspectives in the dimension theory of fractals
Fraser, J. (PI)
1/09/19 → 31/01/23
Project: Standard

Fourier analytic techniques: Fourier analytic techniques in geometry and analysis
Fraser, J. (PI) & Falconer, K. J. (CoI)
1/02/18 → 11/06/21
Project: Standard