Iterated Images and the Plane Jacobian Conjecture
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.
Cite
@article{arxiv.math/0411245,
title = {Iterated Images and the Plane Jacobian Conjecture},
author = {Ronen Peretz and Nguyen Van Chau and Carlos Gutierrez and L. Andrew Campbell},
journal= {arXiv preprint arXiv:math/0411245},
year = {2010}
}
Comments
7 pages, AMSLaTeX, revised in response to referees' suggestions, typos corrected, refrences expanded, to appear in Discrete and Continuous Dynamical Systems