Self-affine sets with fibred tangents

被引：7
|
作者：
Kaenmaki, Antti [1 ]
Koivusalo, Henna [2 ]
Rossi, Eino [1 ]
机构：
[1] Univ Jyvaskyla, Dept Math & Stat, POB 35 MaD, FI-40014 Jyvaskyla, Finland
[2] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England
来源：
ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2017年 / 37卷
基金：
英国工程与自然科学研究理事会;
关键词：
ASSOUAD DIMENSION; SCENERY FLOW; GEOMETRY; DISTRIBUTIONS;
D O I：
10.1017/etds.2015.130
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 O such that all tangent sets at that point are either of the form O((R x C) boolean AND B (0, 1)), where C is a closed porous set, or of the form O((l x {0}) boolean AND B (0, 1)), where l is an interval.
引用
收藏
页码：1915 / 1934
页数：20
相关论文
共 34 条
  • [1] ASSOUAD DIMENSION OF PLANAR SELF-AFFINE SETS
    Barany, Balazs
    Kaenmaki, Antti
    Rossi, Eino
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 374 (02) : 1297 - 1326
  • [2] Dimensions of a class of self-affine Moran sets
    Gu, Yifei
    Miao, Jun Jie
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 513 (01)
  • [3] Assouad-type dimensions of overlapping self-affine sets
    Fraser, Jonathan M.
    Rutar, Alex
    ANNALES FENNICI MATHEMATICI, 2024, 49 (01): : 3 - 21
  • [4] The box dimensions of exceptional self-affine sets in R3
    Fraser, Jonathan M.
    Jurga, Natalia
    ADVANCES IN MATHEMATICS, 2021, 385
  • [5] Two-dimensional self-affine sets with interior points, and the set of uniqueness
    Hare, Kevin G.
    Sidorov, Nikita
    NONLINEARITY, 2016, 29 (01) : 1 - 26
  • [6] ASSOUAD DIMENSION OF SELF-AFFINE CARPETS
    Mackay, John M.
    CONFORMAL GEOMETRY AND DYNAMICS, 2011, 15 : 177 - 187
  • [7] Rigidity of Quasisymmetric Mappings on Self-affine Carpets
    Kaenmaki, Antti
    Ojala, Tuomo
    Rossi, Eino
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2018, 2018 (12) : 3769 - 3799
  • [8] The Assouad dimension of self-affine measures on sponges
    Fraser, Jonathan M.
    Kolossvary, Istvan
    ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2023, 43 (09) : 2974 - 2996
  • [9] ASSOUAD TYPE DIMENSIONS FOR SELF-AFFINE SPONGES
    Fraser, Jonathan M.
    Howroyd, Douglas C.
    ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2017, 42 (01) : 149 - 174
  • [10] AFFINE MAURER-CARTAN INVARIANTS AND THEIR APPLICATIONS IN SELF-AFFINE FRACTALS
    Yang, Yun
    Yu, Yanhua
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2018, 26 (04)
1234