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math.DS2021
The Poincaré exponent and the dimensions of Kleinian limit sets
Jonathan M. Fraser
We provide a proof of the (well-known) result that the Poincaré exponent of a non-elementary Kleinian group is a lower bound for the upper box dimension of the limit set. Our proof…
math.DS2021
Dimensions of Kleinian orbital sets
Thomas Bartlett, Jonathan M. Fraser
Given a non-empty 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…
math.DS2021
Intermediate dimensions of infinitely generated attractors
Amlan Banaji, Jonathan M. Fraser
We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of contractions. Our primary focus is on the intermediate dimensi…