  Below we consider the evolutes of plane real-algebraic curves and discuss
some of their complex and real-algebraic properties. In particular, for a given
degree $d\ge 2$, we provide lower bounds for the following four numerical
invariants: 1) the maximal number of times a real line can intersect the
evolute of a real-algebraic curve of degree $d$; 2) the maximal number of real
cusps which can occur on the evolute of a real-algebraic curve of degree $d$;
3) the maximal number of (cru)nodes which can occur on the dual curve to the
evolute of a real-algebraic curve of degree $d$; 4) the maximal number of
(cru)nodes which can occur on the evolute of a real-algebraic curve of degree
$d$.
