Quasi-locally finite polynomial endomorphisms |
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Authors: | Jean-Philippe Furter |
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Institution: | (1) Department of Mathematics, University of La Rochelle, av. M. Crépeau, 17000 La Rochelle, France |
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Abstract: | If F is a polynomial endomorphism of , let denote the field of rational functions such that . We will say that F is quasi-locally finite if there exists a nonzero such that p(F) = 0. This terminology comes out from the fact that this definition is less restrictive than the one of locally finite endomorphisms
made in Furter, Maubach (J Pure Appl Algebra 211(2):445–458, 2007). Indeed, F is called locally finite if there exists a nonzero such that p(F) = 0. In the present paper, we show that F is quasi-locally finite if and only if for each the sequence is a linear recurrent sequence. Therefore, this notion is in some sense natural. We also give a few basic results on such
endomorphisms. For example: they satisfy the Jacobian conjecture. |
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Keywords: | Polynomial automorphisms Linear recurrent sequences |
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