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We give here the survey of results on dynamics of skew products of one-dimensional self-maps of n-dimensional \((n\ge 2)\) cells, cylinders and tori. The main attention is paid to the properties of \(C^1\) -smooth \(\varOmega \) -stable maps. We also consider here completely geometrically integrable maps and formulate unsolved problems.

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Skew Products and Geometrically Integrable Maps: Results, Problems and Prospects

  • 会议论文

  • 发表日期：

    2025年

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  • Lyudmila Efremova

摘要

We give here the survey of results on dynamics of skew products of one-dimensional self-maps of n-dimensional \((n\ge 2)\) cells, cylinders and tori. The main attention is paid to the properties of \(C^1\) -smooth \(\varOmega \) -stable maps. We also consider here completely geometrically integrable maps and formulate unsolved problems.