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arXiv · 1810.07101

Bernoulli mapping with hole and a saddle-node scenario of the birth of hyperbolic Smale--Williams attractor

Olga B. Isaeva·Igor R. Sataev
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Abstract

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.

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Olga B. Isaeva, Igor R. Sataev. 2018-10-16. Bernoulli mapping with hole and a saddle-node scenario of the birth of hyperbolic Smale--Williams attractor. https://arxiv.org/abs/1810.07101

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