Dynamics of low-degree rational inner skew-products on T2

SOLA A. L. A. N.; TULLY-DOYLE R. Y. A. N.

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Dynamics of low-degree rational inner skew-products on T2

机译：T2上低度有理内偏积动力学

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We examine iteration of certain skew-products on the bidisk whose components are rational inner functions, with emphasis on simple maps of the form ??(z1, z2) = (0(z1, z2), z2). If 0 has degree 1 in the first variable, the dynamics on each horizontal fiber can be described in terms of M??bius transformations but the global dynamics on the 2torus exhibit some complexity, encoded in terms of certain T2-symmetric polynomials. We describe the dynamical behavior of such mappings ?? and give criteria for different configurations of fixed point curves and rotation belts in terms of zeros of a related one-variable polynomial.

机译：我们检查某些skew-products迭代是理性的内在的bidisk组件功能,强调简单的地图形式?度1在第一个变量,动态每个水平纤维可以被描述M ? ?2环展览一些复杂动力学,编码的某些T2-symmetric多项式。这种映射的? ?不动点曲线的不同配置和旋转皮带的零相关单变量多项式。

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《Annales Polonici Mathematici》 |2022年第3期|249-273|共25页
作者
SOLA A. L. A. N.; TULLY-DOYLE R. Y. A. N.;
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Math Sci Res Inst;

Calif Polytech State Univ San Luis Obispo;

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正文语种英语
中图分类数学;
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Dynamics of low-degree rational inner skew-products on T2

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