一些仿射代数变种上Chebyshev自同态的动力学

Pub Date : 2022-07-08 DOI:10.1215/21562261-10607402

Keisuke Uchimura

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引用次数: 0

摘要

一元Chebyshev多项式是复1-空间上典型的混沌映射。复n空间A上的Chebyshev自同态f也是混沌的。自同态f在商空间A/G上诱导映射，其中G是2（n+1）阶的二面体群。利用不变量理论，我们将A/G作为仿射子变种X嵌入到复m空间中。然后我们在X上有态射g。我们研究了当n=2和n=3时g的混沌性质。

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Dynamics of Chebyshev endomorphisms on some affine algebraic varieties

Chebyshev polynomials in one variable are typical chaotic maps on the complex 1-space. Chebyshev endomorphisms f on the complex n-space A are also chaotic. The endomorphisms f induce mappings on the quotient space A/G, where G is the dihedral group of order 2(n+1). Using invariant theory we embed A/G as an affine subvariety X in the complex m-space. Then we have morphisms g on X. We study the chaotic properties of g when n = 2 and 3.

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