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Visible part of dominated self-affine sets in the plane

Autor: Eino Rossi

Publikováno v: Annales Fennici Mathematici

The dimension of the visible part of self-affine sets, that satisfy domination and a projection condition, is being studied. The main result is that the assouad dimension of the visible part equals to 1 for all directions outside the set of limit dir

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::baa1ff64ecc844ec1e05eca77090b4dd
https://afm.journal.fi/article/view/111129

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Assouad dimension of planar self-affine sets

Autor: Balázs Bárány, Antti Käenmäki, Eino Rossi

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

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0848f25ac1f91310878034e9cd8d6820
https://doi.org/10.1090/tran/8224

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Hölder coverings of sets of small dimension

Autor: Eino Rossi, Pablo Shmerkin

Publikováno v: CONICET Digital (CONICET)
Consejo Nacional de Investigaciones Científicas y Técnicas
instacron:CONICET

We show that a set of small box counting dimension can be covered by a H¨older graph from all but a small set of directions, and give sharp bounds for the dimension of the exceptional set, improving a result of B. Hunt and V. Kaloshin. We observe th

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ea5b188d31c72d5edbd9a0d9ef27c18f
https://doi.org/10.4171/jfg/78

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Fractal percolation and quasisymmetric mappings

Autor: Ville Suomala, Eino Rossi

We study the conformal dimension of fractal percolation and show that, almost surely, the conformal dimension of a fractal percolation is strictly smaller than its Hausdorff dimension.
Comment: 16 pages, 4 figures, minor corrections to previous

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::99acf879ee08ad3c87e78092dd3a0053
http://urn.fi/urn:nbn:fi-fe202301102188

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On measures that improve L-q dimension under convolution

Autor: Eino Rossi, Pablo Shmerkin

The $L^q$ dimensions, for $1
Comment: 19 pages

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::91ed89aba7ef1c632c561044cabd158c
http://hdl.handle.net/10138/325288

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Fractal percolation, porosity, and dimension

Autor: Ville Suomala, Tuomo Ojala, Eino Rossi, Changhao Chen

We study the porosity properties of fractal percolation sets $E\subset\mathbb{R}^d$. Among other things, for all $0
Comment: 29 pages, 8 figures

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0d7c4269b37c3c0864142e709e024ebe
http://arxiv.org/abs/1508.05244

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Weak separation condition, Assouad dimension, and Furstenberg homogeneity

Autor: Eino Rossi, Antti Käenmäki

We consider dimensional properties of limit sets of Moran constructions satisfying the finite clustering property. Just to name a few, such limit sets include self-conformal sets satisfying the weak separation condition and certain sub-self-affine se

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8a1ecafa9f5394e6aca33dbc449ae585
http://arxiv.org/abs/1506.07851

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Self-affine sets with fibered tangents

Autor: Eino Rossi, Henna Koivusalo, Antti Käenmäki

Publikováno v: Kaenmaki, A, Koivusalo, H L L & Rossi, E 2017, ' Self-affine sets with fibred tangents ', Ergodic Theory Dynamical Systems, vol. 37, no. 6, pp. 1915–1934 . https://doi.org/10.1017/etds.2015.130

We study tangent sets of strictly self-affine sets in the plane. If a set in this class satisfies the strong separation condition and projects to a line segment for sufficiently many directions, then for each generic point there exists a rotation $\m

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3d1216bedbdfad43c14df9cb19522b99
http://arxiv.org/abs/1505.00958

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Locally rich compact sets

Autor: Changhao Chen, Eino Rossi

Publikováno v: Illinois J. Math. 58, no. 3 (2014), 779-806

We construct a compact metric space that has any other compact metric space as a tangent, with respect to the Gromov-Hausdorff distance, at all points. Furthermore, we give examples of compact sets in the Euclidean unit cube, that have almost any oth

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ee936634cc075d1150b38b8f249f0a8a

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Local dimensions of measures on infinitely generated self-affine sets

Autor: Eino Rossi

Publikováno v: Journal of Mathematical Analysis and Applications. 413(2):1030

We show the existence of the local dimension of an invariant probability measure on an infinitely generated self-affine set, for almost all translations. This implies that an ergodic probability measure is exactly dimensional. Furthermore the local d

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d49d5ba54835f9c315a212c4fb7c0146
http://juuli.fi/Record/0028781414

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