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True laminations for complex Hènon maps

Pages: 834 - 841, Issue Special, July 2003

 Abstract        Full Text (212.1K)              

Meiyu Su - Mathematics Department Long Island University, Broolyn Campus, University Plaza, Brooklyn, NY 11201, United States (email)

Abstract: 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:  Generalized complex Hènon maps, Stable and unstable manifolds, Measured Riemann surface laminations, Pesin boxes, and Entropy topology.
Mathematics Subject Classification:  Mathematics Subject Classification

Received: August 2002;      Revised: April 2003;      Published: April 2003.