Hausdorff dimension of Cantor attractors in one-dimensional dynamics

被引：0
|
作者：
Simin Li
Weixiao Shen
机构：
[1] University of Science and Technology of China,Mathematics Department
来源：
Inventiones mathematicae | 2008年 / 171卷
关键词：
Periodic Point; Hausdorff Dimension; Return Time; Universal Constant; Admissible Pair;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we study the Hausdorff dimension of Cantor attractors of smooth interval maps with non-flat critical points. We prove that the Hausdorff dimension is bounded from above by a constant less than 1 which depends only on the number and order of the critical points.
引用
收藏
页码：345 / 387
页数：42
相关论文
共 50 条
  • [21] On the Hausdorff dimension of piecewise hyperbolic attractors
    Persson, Tomas
    FUNDAMENTA MATHEMATICAE, 2010, 207 (03) : 255 - 272
  • [22] On the Hausdorff Dimension of Some Random Cantor Sets
    V. Paulauskas
    R. Zovė
    Lithuanian Mathematical Journal, 2003, 43 (2) : 189 - 198
  • [23] Hausdorff dimension of Besicovitch sets of Cantor graphs
    Altaf, Iqra
    Csoernyei, Marianna
    Hera, Kornelia
    MATHEMATIKA, 2024, 70 (02)
  • [24] Cantor Julia sets with Hausdorff dimension two
    Yang, Fei
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2021, 2021 (07) : 4994 - 5006
  • [25] ON THE HAUSDORFF DIMENSION FAITHFULNESS AND THE CANTOR SERIES EXPANSION
    Albeverio, S.
    Ivanenko, Ganna
    Lebid, Mykola
    Torbin, Grygoriy
    METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, 2020, 26 (04): : 298 - 310
  • [26] Hausdorff dimension of Cantor sets and polynomial hulls
    Jöricke, B
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 134 (05) : 1347 - 1354
  • [27] SILVER MEAN HAUSDORFF DIMENSION AND CANTOR SETS
    ELNASCHIE, MS
    CHAOS SOLITONS & FRACTALS, 1994, 4 (10) : 1861 - 1869
  • [28] A function whose graph is of dimension 1 and has locally an infinite one-dimensional Hausdorff measure
    Liu, YY
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 332 (01): : 19 - 23
  • [29] On the finiteness of attractors for one-dimensional maps with discontinuities
    Brandao, P.
    Palis, J.
    Pinheiro, V
    ADVANCES IN MATHEMATICS, 2021, 389
  • [30] Coexistence of attractors in a one-dimensional CNN array
    Galias, Z
    Ogorzalek, MJ
    CNNA 98 - 1998 FIFTH IEEE INTERNATIONAL WORKSHOP ON CELLULAR NEURAL NETWORKS AND THEIR APPLICATIONS - PROCEEDINGS, 1998, : 118 - 123
12345