A new construction of the unstable manifold for the measure-preserving H{é}non map

Jensen, Erik

doi:10.1090/S0002-9939-07-09045-4

A new construction of the unstable manifold for the measure-preserving H{é}non map
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Proc. Amer. Math. Soc. 136 (2008), 181-192 Request permission

Abstract:

Let $H$ denote the measure-preserving Hénon map with the parameter $a > 0$. The map $H$ 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, \[ W^u(\boldsymbol {p}) = \lim _{n\to \infty } H^n(\mathcal L) \] where $\mathcal L$ is the line $y=-x$ and $W^u(\boldsymbol {p})$ denotes the unstable manifold of $\boldsymbol {p}$.

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