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pro vyhledávání: '"Kenneth J. Falconer"'
Autor:
Kenneth J. Falconer
Publikováno v:
Bulletin of the London Mathematical Society. 54:318-333
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f33019e23af35e9dcb4c4ca85bd1d561
https://doi.org/10.1112/blms.12554
https://doi.org/10.1112/blms.12554
Publikováno v:
Journal of Fractal Geometry. 8:95-116
Intermediate dimensions were recently introduced to interpolate between the Hausdorff and box-counting dimensions of fractals. Firstly, we show that these intermediate dimensions may be defined in terms of capacities with respect to certain kernels.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::82f2f38c2aaf6ea1e1cc6079edefc5df
https://doi.org/10.4171/jfg/99
https://doi.org/10.4171/jfg/99
Publikováno v:
Ergodic Theory and Dynamical Systems. 41:3288-3306
We study the $L^{q}$ -spectrum of measures in the plane generated by certain nonlinear maps. In particular, we consider attractors of iterated function systems consisting of maps whose components are $C^{1+\alpha }$ and for which the Jacobian is a lo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0b20103955eb53cf4ccf60e2efff235d
https://doi.org/10.1017/etds.2020.106
https://doi.org/10.1017/etds.2020.106
Autor:
Kenneth J. Falconer
We show that the almost sure θ -intermediate dimension of the image of the set F p = { 0 , 1 , 1 2 p , 1 3 p , … } under index- h fractional Brownian motion is θ p h + θ , a value that is smaller than that given by directly applying the Holder b
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0b1649a40223a87f4d3bab9eeb18a531
http://arxiv.org/abs/2108.12306
http://arxiv.org/abs/2108.12306
Autor:
Xiong Jin, Kenneth J. Falconer
Publikováno v:
Falconer, K & Jin, X 2019, ' Exact dimensionality and projection properties of Gaussian multiplicative chaos measures ', Transactions of the American Mathematical Society, vol. 372, no. 4, pp. 2921–2957 . https://doi.org/10.1090/tran/7776
Given a measure $\nu$ on a regular planar domain $D$, the Gaussian multiplicative chaos measure of $\nu$ studied in this paper is the random measure ${\widetilde \nu}$ obtained as the limit of the exponential of the $\gamma$-parameter circle averages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8dbfc2217b7ff47845a4b491e7cfe6d5
https://doi.org/10.1090/tran/7776
https://doi.org/10.1090/tran/7776
Autor:
Kenneth J. Falconer
Publikováno v:
Lecture Notes in Mathematics ISBN: 9783030748623
This article surveys the $\theta$-intermediate dimensions that were introduced recently which provide a parameterised continuum of dimensions that run from Hausdorff dimension when $\theta=0$ to box-counting dimensions when $\theta=1$. We bring toget
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ed92025a1d0e329d1178ec6067e6e28d
http://arxiv.org/abs/2011.04363
http://arxiv.org/abs/2011.04363
Autor:
Kenneth J. Falconer
Dimension profiles were introduced by Falconer and Howroyd to provide formulae for the box-counting and packing dimensions of the orthogonal projections of a set E or a measure on Euclidean space onto almost all m-dimensional subspaces. The original
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ea6c4003023094be2cb7244798c41a0a
https://doi.org/10.1142/9789811215537_0001
https://doi.org/10.1142/9789811215537_0001
We present several applications of the Assouad dimension, and the related quasi-Assouad dimension and Assouad spectrum, to the box and packing dimensions of orthogonal projections of sets. For example, we show that if the (quasi-)Assouad dimension of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dbcc0b6602647c0de178e92c33fb0209
http://arxiv.org/abs/1911.04857
http://arxiv.org/abs/1911.04857
Autor:
Kenneth J. Falconer
Dimension profiles were introduced in [8,11] to give a formula for the box-counting and packing dimensions of the orthogonal projections of a set $R^n$ onto almost all $m$-dimensional subspaces. However, these definitions of dimension profiles are in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1a1050d4a397179cab33cfc999d05b5d
http://arxiv.org/abs/1901.11014
http://arxiv.org/abs/1901.11014
Autor:
Kenneth J. Falconer, Pertti Mattila
Publikováno v:
Journal of Fractal Geometry. 3:319-329
We present strong versions of Marstrand's projection theorems and other related theorems. For example, if E is a plane set of positive and finite s-dimensional Hausdorff measure, there is a set X of directions of Lebesgue measure 0, such that the pro
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f7780db125864e7e4a30679ef0672b11
https://doi.org/10.4171/jfg/38
https://doi.org/10.4171/jfg/38