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Iterated Images and the Plane Jacobian Conjecture

Ronen Peretz·Nguyen Van Chau·Carlos Gutierrez·L. Andrew Campbell
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Abstract

We show that the iterated images of a Jacobian pair stabilize; that is, the k-th iterates of a polynomial map of complex two-space to itself with a nonzero constant Jacobian determinant all have the same image for sufficiently large k. More generally, we obtain the same result for open polynomial maps of a closed algebraic subset X of complex N-space to itself that have finite coimage, and for cofinite subsets of such an X invariant under the map. We apply these results to obtain a new characterization of the two dimensional complex Jacobian conjecture related to questions of surjectivity.

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Ronen Peretz, Nguyen Van Chau, Carlos Gutierrez, L. Andrew Campbell. 2005-08-27. Iterated Images and the Plane Jacobian Conjecture. https://arxiv.org/abs/math/0411245

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