  Three dimensional analytic H\'enon-like map $$ F(x,y,z) = (f(x) -
\epsilon(x,y,z),\, x,\, \delta(x,y,z)) $$ and its {\em period doubling}
renormalization is defined. If $ F $ is infinitely renormalizable map, Jacobian
determinant of $ n^{th} $ renormalized map, $ R^nF $ has asymptotically
universal expression $$ Jac R^nF = b_F^{2^n}a(x)(1 + O(\rho^n)) $$ where $ b_F
$ is the average Jacobian of $ F $. The toy model map, $ F_{mod} $ is defined
as the map satisfying $ \partial_z \epsilon \equiv 0 $. The set of toy model
map is invariant under renormalizaton. Moreover, if $ \| \partial_z \delta \|
\ll \| \partial_y \epsilon \| $, then there exists the continuous invariant
plane field over $ \mathcal O_F $ with dominated splitting. Under this
condition, three dimensional H\'enon-like map %with the dominated splitting is
dynamically decomposed into two dimensional map with contraction along the
strong stable direction. Any invariant line field on this plane filed over $
\mathcal O_{F_{mod}} $ cannot be continuous.
