  In this work we consider the asymptotic behavior of the nonlinear semigroup
defined by a semilinear parabolic problem with homogeneous Neumann boundary
conditions posed in a bounded region of the plane that degenerates into a line
segment when a positive parameter $\epsilon$ goes to zero (a thin domain). Here
we also allow that its boundary presents highly oscillatory behavior with
different orders and variable profile. We take thin domains possessing the same
order $\epsilon$ to the thickness and amplitude of the oscillations but
assuming different order to the period of oscillations on the top and the
bottom of the boundary. We combine methods from linear homogenization theory
and the theory on nonlinear dynamics of dissipative systems to obtain the limit
problem establishing convergence properties for the solutions. At the end we
show the upper semicontinuity of the attractors and stationary states.
