Estimates of the fractal and Hausdorff dimensions of sets invariant under multimappings

被引:3
|
作者
Mel'nik, VS [1 ]
机构
[1] VM Glushkov Cybernet Inst, UA-252207 Kiev, Ukraine
关键词
multimapping; Banach space; invariant subset; Hausdorff dimension; fractal dimension; attractors;
D O I
10.1007/BF02308758
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We obtain estimates for the Hausdorff and fractal dimensions of sets A subset of X invariant under multimappings F: X --> 2(X) of a Banach space X into the power set of X.
引用
收藏
页码:190 / 196
页数:7
相关论文
共 50 条
  • [1] Estimates of the fractal and hausdorff dimensions of sets invariant under multimappings
    V. S. Mel'nik
    [J]. Mathematical Notes, 1998, 63 : 190 - 196
  • [2] Hausdorff and Fractal Dimension Estimates for Invariant Sets of Non-Injective Maps
    Boichenko, V. A.
    Franz, A.
    Leonov, G. A.
    Reitmann, V.
    [J]. ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 1998, 17 (01): : 207 - 223
  • [3] On estimates of the Hausdorff dimension of invariant compact sets
    Pogromsky, AY
    Nijmeijer, H
    [J]. NONLINEARITY, 2000, 13 (03) : 927 - 945
  • [4] Hausdorff dimensions of sofic affine-invariant sets
    Kenyon, R
    Peres, Y
    [J]. ISRAEL JOURNAL OF MATHEMATICS, 1996, 94 : 157 - 178
  • [5] Hausdorff dimensions of sofic affine-invariant sets
    R. Kenyon
    Y. Peres
    [J]. Israel Journal of Mathematics, 1997, 97 : 347 - 347
  • [6] Hausdorff dimension estimates for invariant sets of piecewise smooth maps
    Reitmann, V
    Schnabel, U
    [J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2000, 80 (09): : 623 - 632
  • [7] Upper Estimates for the Hausdorff Dimension of Negatively Invariant Sets of Local Cocycles
    Leonov, G. A.
    Reitmann, V.
    Slepukhin, A. S.
    [J]. DOKLADY MATHEMATICS, 2011, 84 (01) : 551 - 554
  • [8] On Upper Estimates for the Hausdorff Dimension of Negatively Invariant Sets of Local Cocycles
    Reitmann, F.
    Slepukhin, A. S.
    [J]. VESTNIK ST PETERSBURG UNIVERSITY-MATHEMATICS, 2011, 44 (04) : 292 - 300
  • [9] Hausdorff dimension estimates for invariant sets with an equivariant tangent bundle splitting
    Franz, A
    [J]. NONLINEARITY, 1998, 11 (04) : 1063 - 1074
  • [10] Upper estimates for the hausdorff dimension of negatively invariant sets of local cocycles
    G. A. Leonov
    V. Reitmann
    A. S. Slepukhin
    [J]. Doklady Mathematics, 2011, 84 : 551 - 554