Dimension of a class of intrinsically transversal solenoidal attractors in high dimensions

2022/05/11 by Ricardo Gião Bortolotti, Bortolotti, Ricardo, Eberson Ferreira da Silva +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2205.05437

openalex publication_date 2022/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the fractal dimension of a class of solenoidal attractors in dimensions greater or equal than 3, proving that if the contraction is sufficiently strong, the expansion is close to conformal and the attractor satisfy a geometrical condition of transversality between its components, then the Hausdorff and box-counting dimension of every stable section of the attractor have the same value, which corresponds to the zero of the topological pressure as in Bowen's formula. We also calculate the dimension of the attractor and prove that it is continuous in this class.

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