  We consider a family of $(2,1)$-rational functions given on the set of
$p$-adic field $Q_p$. Each such function has a unique fixed point. We study
ergodicity properties of the dynamical systems generated by $(2,1)$-rational
functions. For each such function we describe all possible invariant spheres.
We characterize ergodicity of each $p$-adic dynamical system with respect to
Haar measure reduced on each invariant sphere. In particular, we found an
invariant spheres on which the dynamical system is ergodic and on all other
invariant spheres the dynamical systems are not ergodic.
