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 $\boldsymbol {p}$.References
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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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 181-192
- MSC (2000): Primary 37D10
- DOI: https://doi.org/10.1090/S0002-9939-07-09045-4
- MathSciNet review: 2350403