Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Antti Käenmäki"'
Publikováno v:
Transactions of the American Mathematical Society. 374:1297-1326
We calculate the Assouad dimension of a planar self-affine set $X$ satisfying the strong separation condition and the projection condition and show that $X$ is minimal for the conformal Assouad dimension. Furthermore, we see that such a self-affine s
Autor:
Jonathan M. Fraser, Antti Käenmäki
Publikováno v:
Proceedings of the American Mathematical Society. 148:3393-3405
We prove that for an arbitrary upper semi-continuous function $\phi\colon G(1,2) \to [0,1]$ there exists a compact set $F$ in the plane such that $\dim_{\textrm{A}} \pi F = \phi(\pi)$ for all $\pi \in G(1,2)$, where $\pi F$ is the orthogonal projecti
Publikováno v:
Bárány, B, Jordan, T, Käenmäki, A & Rams, M 2020, ' Birkhoff and Lyapunov spectra on planar self-affine sets ', International Mathematics Research Notices, vol. 0, rnz359 . https://doi.org/10.1093/imrn/rnz359
Working on strongly irreducible planar self-affine sets satisfying the strong open set condition, we calculate the Birkhoff spectrum of continuous potentials and the Lyapunov spectrum.
Comment: 32 pages, 1 figure
Comment: 32 pages, 1 figure
The purpose of this article is to introduce and motivate the notion of Minkowski (or box) dimension for measures. The definition is simple and fills a gap in the existing literature on the dimension theory of measures. As the terminology suggests, we
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1690ba6722e394af52a967a7d16f7cb4
http://arxiv.org/abs/2001.07055
http://arxiv.org/abs/2001.07055
Publikováno v:
Journal of the London Mathematical Society. 98:223-252
An affine iterated function system is a finite collection of affine invertible contractions and the invariant set associated to the mappings is called self-affine. In 1988, Falconer proved that, for given matrices, the Hausdorff dimension of the self
Autor:
Ian Morris, Antti Käenmäki
Publikováno v:
Proceedings of the London Mathematical Society. 116:929-956
A fundamental problem in the dimension theory of self-affine sets is the construction of high- dimensional measures which yield sharp lower bounds for the Hausdorff dimension of the set. A natural strategy for the construction of such high-dimensiona
Autor:
Bing Li, Antti Käenmäki
Publikováno v:
Statistics & Probability Letters. 126:18-25
We prove that generically, for a self-affine set in $\mathbb{R}^d$, removing one of the affine maps which defines the set results in a strict reduction of the Hausdorff dimension. This gives a partial positive answer to a folklore open question.
We investigate how the Hausdorff dimensions of microsets are related to the dimensions of the original set. It is known that the maximal dimension of a microset is the Assouad dimension of the set. We prove that the lower dimension can analogously be
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b63b5113186c76085564dda4d5032042
https://hdl.handle.net/10023/17296
https://hdl.handle.net/10023/17296
Autor:
Antti Käenmäki, Balázs Bárány
We exhibit self-similar sets on the line which are not exponentially separated and do not generate any exact overlaps. Our result shows that the exponential separation, introduced by Hochman in his groundbreaking theorem on the dimension of self-simi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8b87201072aa07c5e8a6e90559c1ffd7
Publikováno v:
Nonlinearity. 29:807-822
We study the dimensional properties of Moran sets and Moran measures in doubling metric spaces. In particular, we consider local dimensions and $L^q$-dimensions. We generalize and extend several existing results in this area.
Comment: 13 pages
Comment: 13 pages