  In this paper we consider function $f(x)={x+a\over bx+c}$, (where $b\ne 0$,
$c\ne ab$, $x\ne -{c\over b}$) on three fields: the set of real, $p$-adic and
complex numbers. We study dynamical systems generated by this function on each
field separately and give some comparison remarks.
  For real variable case we show that the real dynamical system of the function
depends on the parameters $(a,b,c)\in \mathbb R^3$. Namely, we classify the
parameters to three sets and prove that: for the parameters from first class
each point, for which the trajectory is well defined, is a periodic point of
$f$; for the parameters from second class any trajectory (under $f$) converges
to one of fixed points (there may be up to two fixed points); for the
parameters from third class any trajectory is dense in $\mathbb R$.
  For the $p$-adic variable we give a review of known results about dynamical
systems of function $f$. Then using a recently developed method we give simple
new proofs of these results and prove some new ones related to trajectories
which do not converge.
  For the complex variables we give a review of known results.
