Bypassing dynamical systems : A simple way to get the box-counting\n dimension of the graph of the Weierstrass function

2017/11/26 by Claire David, David, Claire
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1711.10349

openalex publication_date 2017/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the following, bypassing dynamical systems tools, we propose a simple\nmeans of computing the box dimension of the graph of the classical Weierstrass\nfunction defined, for any real number~x, by~ cal W(x)= n\∑_n=0^+\∞ \λⁿ ,\cos ( 2 , \π ,N_bⁿ ,x \)\n , where~\λ and~N_b are two real numbers such that~$0\n<\λ<1,~$ N_b ,\∈ , N and~ \λ ,N_b > 1 , using a sequence\na graphs that approximate the studied one.\n

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