Article ID Journal Published Year Pages File Type
4598242 Journal of Pure and Applied Algebra 2007 14 Pages PDF
Abstract

We study polynomial endomorphisms FF of CNCN which are locally finite in the following sense: the vector space generated by r∘Fnr∘Fn (n≥0n≥0) is finite dimensional for each r∈C[x1,…,xN]r∈C[x1,…,xN]. We show that such endomorphisms exhibit similar features to linear endomorphisms: they satisfy the Jacobian Conjecture, have vanishing polynomials, admit suitably defined minimal and characteristic polynomials, and the invertible ones admit a Dunford decomposition into “semisimple” and “unipotent” constituents. We also explain a relationship with linear recurrent sequences and derivations. Finally, we give particular attention to the special cases where FF is nilpotent and where N=2N=2.

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Physical Sciences and Engineering Mathematics Algebra and Number Theory
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