2018/10/16 by О. Б. Исаева, Isaeva, Olga B., I. R. Sataev +1
Computer Science · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.1810.07101
openalex publication_date 2018/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One-dimensional Bernoulli mapping with hole is suggested to describe the regularities of the appearance of a chaotic set under the saddle-node scenario of the birth of the Smale--Williams hyperbolic attractor. In such a mapping, a non-trivial chaotic set (with non-zero Hausdorff dimension) arises in the general case as a result of a cascade of period-adding bifurcations characterized by geometric scaling both in the phase space and in the parameter space. Numerical analysis of the behavior of models demonstrating the saddle-node scenario of birth of a hyperbolic chaotic Smale--Williams attractor shows that these regularities are preserved in the case of multidimensional systems. Limits of applicability of the approximate 1D model are discussed.