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arXiv · 2207.03657

Dynamics of Chebyshev endomorphisms on some affine algebraic varieties

Keisuke Uchimura
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Abstract

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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Keisuke Uchimura. 2022-07-08. Dynamics of Chebyshev endomorphisms on some affine algebraic varieties. https://arxiv.org/abs/2207.03657

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