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A new construction of the unstable manifold for the measure-preserving Hénon map

Authors:	Erik Jensen

Institution:	Department of Mathematics and Statistics, Jeffery Hall, Queen's University, Kingston, Ontario, Canada K7L~3N6

Abstract:	Let denote the measure-preserving Hénon map with the parameter . The map has a hyperbolic fixed point $\boldsymbol{p}$ . The main result of this paper is that the unstable mainfold of $\boldsymbol{p}$ is the iterated limit of a very simple set. Informally, $\displaystyle W^u(\boldsymbol{p}) = \lim_{n\to\infty} H^n(\mathcal L)$ where $\mathcal L$ is the line and $W^u(\boldsymbol{p})$ denotes the unstable manifold of $\boldsymbol{p}$ .

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