Box dimension of the graphs of the generalized Weierstrass-type functions

DOI10.3934/dcds.2023068arXiv2210.12434OpenAlexW4382399807MaRDI QIDQ6165950

Haojie Ren

Publication date: 2 August 2023

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2210.12434

zbMATH Keywords

strange attractorsbox dimensionfractal geometrydimension theoryWeierstrass-type functions

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Fractals (28A80)

Cites Work

• On the dimension of the graph of the classical Weierstrass function
• On self-similar sets with overlaps and inverse theorems for entropy
• Hausdorff dimension of the graphs of the classical Weierstrass functions
• On the random series \(\sum\pm\lambda^ n\) (an Erdös problem)
• A dichotomy for the Weierstrass-type functions
• On the dimension of Bernoulli convolutions for all transcendental parameters
• Hausdorff dimension of planar self-affine sets and measures
• Fat solenoidal attractors
• On the Hausdorff dimension of some fractal sets
• The Lyapunov dimension of a nowhere differentiable attracting torus
• On the Hausdorff Dimension of Some Graphs
• The Hausdorff dimension of self-affine fractals
• Fractal Dimensions and Singularities of the Weierstrass Type Functions
• The Hausdorff dimension of graphs of Weierstrass functions
• Sets of Fractional Dimensions (V): on Dimensional Numbers of Some Continuous Curves
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