Fractal Dimension of Graphs of Typical Continuous Functions on Manifolds

被引：0
|
作者：
Mirzaie, Reza [1 ]
机构：
[1] Imam Khomeini Int Univ, Fac Sci, Dept Pure Math, Qazvin, Iran
来源：
IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS | 2018年 / 13卷 / 02期
关键词：
Manifold; Fractal; Box dimension;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
If M is a compact Riemannian manifold and C(M, R) is the set of all real valued continuous functions defined on M, then we show that for typical element f is an element of C(M, R), (dim) over bar (B) (graph(f)) is as big as possible and for typical f is an element of C(M, R), (dim) under bar (B)(graph(f)) is as small as possible.
引用
收藏
页码：93 / 99
页数：7
相关论文
共 50 条
  • [1] Graphs of continuous functions and fractal dimensions
    Verma, Manuj
    Priyadarshi, Amit
    CHAOS SOLITONS & FRACTALS, 2023, 172
  • [2] On the box dimensions of graphs of typical continuous functions
    Hyde, J.
    Laschos, V.
    Olsen, L.
    Petrykiewicz, I.
    Shaw, A.
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 391 (02) : 567 - 581
  • [3] On the average box dimensions of graphs of typical continuous functions
    B. Adam-Day
    C. Ashcroft
    L. Olsen
    N. Pinzani
    A. Rizzoli
    J. Rowe
    Acta Mathematica Hungarica, 2018, 156 : 263 - 302
  • [4] On the average box dimensions of graphs of typical continuous functions
    Adam-Day, B.
    Ashcroft, C.
    Olsen, L.
    Pinzani, N.
    Rizzoli, A.
    Rowe, J.
    ACTA MATHEMATICA HUNGARICA, 2018, 156 (02) : 263 - 302
  • [5] A note on fractal dimensions of graphs of certain continuous functions
    Liu, Peizhi
    Yu, Binyan
    Liang, Yongshun
    CHAOS SOLITONS & FRACTALS, 2024, 188
  • [6] Fractal dimension of Katugampola fractional integral of continuous functions with unbounded variation
    Peng, Wenliang
    Yao, Kui
    Liang, Yongshun
    PROCEEDINGS OF THE 2019 31ST CHINESE CONTROL AND DECISION CONFERENCE (CCDC 2019), 2019, : 1398 - 1402
  • [7] FRACTAL DIMENSIONS OF LINEAR COMBINATION OF CONTINUOUS FUNCTIONS WITH THE SAME BOX DIMENSION
    Wang, Xuefei
    Zhao, Chunxia
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2020, 28 (07)
  • [8] Fractal dimension of Hadamard fractional integral of continuous functions with countable UV points
    Wu, Xiao Er
    Shun-Liang, Yong
    Zhu, Ya Hui
    PROCEEDINGS OF THE 30TH CHINESE CONTROL AND DECISION CONFERENCE (2018 CCDC), 2018, : 1636 - 1641
  • [9] Fractal Dimension of α-Fractal Functions Without Endpoint Conditions
    Gurubachan
    Chandramouli, V. V. M. S.
    Verma, S.
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2024, 21 (03)
  • [10] A note on stability and fractal dimension of bivariate α-fractal functions
    V. Agrawal
    T. Som
    S. Verma
    Numerical Algorithms, 2023, 93 : 1811 - 1833
12345