True laminations for complex Hènon maps

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2003, 2003(Special): 834-841. doi: 10.3934/proc.2003.2003.834

True laminations for complex Hènon maps

1.	Mathematics Department Long Island University, Broolyn Campus, University Plaza, Brooklyn, NY 11201, United States

Received August 2002 Revised April 2003 Published April 2003

Abstract
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In this paper, we are specially interested in the lamination structure for a polynomial diffeomorphism $f$ of $\mathbb(C)^2$ that are conjugate to a finite decomposition of generalized complex Hènon maps on $\mathbb(C)$. We prove that there are true $f$-invariant contracting and expanding measured Riemann surface laminations–injected into the stable and unstable partitions $W^(s/u)$. Leaves of the laminations are conformally isomorphic to the complex plane $\mathbb(C)$. The new ingredients here are the countable collection of the Pesin boxes and a $\sigma$-finite topology, the ‘entropy topology’ on the transversals, defined by the logarithm of the measures obtained by conditioning the unique ergodic measure of maximal entropy $\mu$.

Keywords: Measured Riemann surface laminations, Stable and unstable manifolds, and Entropy topology., Generalized complex Hènon maps, Pesin boxes.

Mathematics Subject Classification: Mathematics Subject Classification.

Citation: Meiyu Su. True laminations for complex Hènon maps. Conference Publications, 2003, 2003 (Special) : 834-841. doi: 10.3934/proc.2003.2003.834

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