1986/09/22 by Kwok Yeung Tsang · 1 citation
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Chaos control and synchronization #Quantum chaos and dynamical systems #Attractor #Hausdorff dimension #Curse of dimensionality #Cartesian product #Cantor set #Set (abstract data type) #Dimension (graph theory) #Product (mathematics) #Hausdorff space #Effective dimension #Fractal dimension #Cartesian coordinate system #Pure mathematics #Fractal #Mathematics #Mathematical analysis #Statistical physics #Physics #Computer science #Geometry #Discrete mathematics #Statistics
paper · doi:10.1103/physrevlett.57.1390
openalex publication_date 1986/09/22 · openalex created_date 2016/06/24 · openalex updated_date 2025/11/06
An analytical method to determine the dimensionality of strange attractors in two-dimensional maps is introduced. In this method, the geometric structures of an attractor are obtained from a procedure developed previously. Such structures often appear to be the Cartesian product of a curve and a Cantor set. From the geometric structures, we determine the Hausdorff dimension first for the Cantor set, and then for the attractor. The results compare well with numerical results obtained for the H'enon, Zaslavskii, and Kaplan-Yorke maps.