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


Author: Erik Jensen
Journal: Proc. Amer. Math. Soc. 136 (2008), 181-192
MSC (2000): Primary 37D10
DOI: https://doi.org/10.1090/S0002-9939-07-09045-4
Published electronically: October 4, 2007
MathSciNet review: 2350403
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Abstract | References | Similar Articles | Additional Information

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,

$\displaystyle 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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Additional Information

Erik Jensen
Affiliation: Department of Mathematics and Statistics, Jeffery Hall, Queen’s University, Kingston, Ontario, Canada K7L 3N6
Email: jensene@mast.queensu.ca

DOI: https://doi.org/10.1090/S0002-9939-07-09045-4
Received by editor(s): June 12, 2006
Received by editor(s) in revised form: September 29, 2006
Published electronically: October 4, 2007
Additional Notes: The author would like to thank Leo Jonker for his helpful suggestions
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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