{\bf Abstract}

Isometries on formal power series over the finite field $\ff_2$
or on $2$--adic integers can be
computed by invertible transducers on inputs from $\{0,1\}^\infty$.
We consider the structural complexity of an isometry $f$,
measured as {\it tree complexity} $T(f,h)$, $h$ the tree height
[H.~Niederreiter, M.~Vielhaber, {\it J.~Cpx.}, ... more >>>