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Autor:
Fraser, Jonathan M., Stuart, Liam
We prove that the Assouad dimension of a parabolic Julia set is $\max\{1,h\}$ where $h$ is the Hausdorff dimension of the Julia set. Since $h$ may be strictly less than 1, this provides examples where the Assouad and Hausdorff dimension are distinct.
Externí odkaz:
http://arxiv.org/abs/2203.04943
Autor:
Fraser, Jonathan M., Stuart, Liam
Publikováno v:
Geometriae Dedicata, 217, (2023), Paper No. 1, 32 pp
The Assouad dimension of the limit set of a geometrically finite Kleinian group with parabolics may exceed the Hausdorff and box dimensions. The Assouad \emph{spectrum} is a continuously parametrised family of dimensions which `interpolates' between
Externí odkaz:
http://arxiv.org/abs/2203.04931
Autor:
Fraser, Jonathan M., Stuart, Liam
Publikováno v:
Annales Fennici Mathematici, 48, (2023), 325-344
Parabolic fixed points form a countable dense subset of the limit set of a non-elementary geometrically finite Kleinian group with at least one parabolic element. Given such a group, one may associate a standard set of pairwise disjoint horoballs, ea
Externí odkaz:
http://arxiv.org/abs/2202.09178
Autor:
Fraser, Jonathan M., Stuart, Liam
Publikováno v:
Bulletin of the American Mathematical Society, 61, (2024), 103-118
The Sullivan dictionary provides a beautiful correspondence between Kleinian groups acting on hyperbolic space and rational maps of the extended complex plane. An especially direct correspondence exists concerning the dimension theory of the associat
Externí odkaz:
http://arxiv.org/abs/2007.15493
Autor:
Fraser, Jonathan M.1 (AUTHOR), Stuart, Liam1 (AUTHOR)
Publikováno v:
Bulletin (New Series) of the American Mathematical Society. Jan2024, Vol. 61 Issue 1, p103-118. 16p.
Akademický článek
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Autor:
Stuart, Liam
This thesis includes work from four papers that were written during the author’s time as a PhD student with Jonathan Fraser, namely [40, 41, 42, 43]. Chapter 1 introduces the two main settings that will be studied throughout this thesis along with
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::da69c48c9d63affad990d1d173eba190
Autor:
Fraser, Jonathan M., Stuart, Liam
Publikováno v:
Annales Fennici Mathematici
Parabolic fixed points form a countable dense subset of the limit set of a non-elementary geometrically finite Kleinian group with at least one parabolic element. Given such a group, one may associate a standard set of pairwise disjoint horoballs, ea
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4bad4a2f0ccf8b1f76f93ff712d1d8c7
https://hdl.handle.net/10023/27566
https://hdl.handle.net/10023/27566
Akademický článek
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