True laminations for complex Hènon maps

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 $\mu$.