  We define a semidirect product groupoid of a system of partially defined
local homeomorphisms $T=(T_{1},..., T_{r})$. We prove that this construction
gives rise to amenable groupoids. The associated algebra is a Cuntz-like
algebra. We use this construction for higher rank graph algebras in order to
give a topological interpretation for the duality in $E$-theory between
$C^{*}(\Lambda)$ and $C^{*}(\Lambda^{op})$.

Operator Algebras;Dynamical Systems