A toral diffeomorphism with a non-polygonal rotation set
英文摘要:
We construct a diffeomorphism of the two-dimensional torus which is isotopic to the identity and whose rotation set is not a polygon.
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Jaroslaw Kwapisz
We construct a diffeomorphism of the two-dimensional torus which is isotopic to the identity and whose rotation set is not a polygon.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
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We show that, for pairs of hyperbolic toral automorphisms on the $2$-torus, the points with dense forward orbits under one map and nondense forward orbits under the other is a dense, uncountable set. The pair of maps can be noncommuting. We also show the same for pairs of $C^2$-Anosov diffeomorphisms on the $2$-torus. (The pairs must satisfy slight constraints.) Our main tools are the Baire Category theorem and a geometric construction that allows us to give a geometric characterization of the fractal that is the set of points with forward orbits that miss a certain open set.
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本文研究环面微分同胚旋转集的圆度,定义 Kwapisz 型映射旋转集的圆度比值,并给出其上下界,发现该比值非单调且不连续。
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