确定性混沌博弈中收敛速度可变的拓扑普遍性

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Pub Date : 2024-08-30 DOI:10.1007/s13398-024-01658-0

Krzysztof Leśniak, Nina Snigireva, Filip Strobin

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摘要

设 A 是完整空间上一个巴拿赫收缩迭代函数系统（IFS）的吸引子。我们证明，由典型（在贝雷范畴的意义上）驱动器产生的轨道能以各种可能的速度恢复 A。我们的结果扩展了论文中的结果：Leśniak et al. (Chaos 32(1):013110, 2022).我们还证明了我们的结果在某种程度上是最优的。

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Topological prevalence of variable speed of convergence in the deterministic chaos game

Let A be the attractor of a Banach contractive iterated function system (IFS) on a complete space. We prove that the orbit generated by a typical (in the sense of Baire category) driver recovers A with every possible speed. Our result extends the one from the paper: Leśniak et al. (Chaos 32(1):013110, 2022). We also show that our result is optimal from a certain point of view.

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas

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