  A family of non-conjugate chaotic maps generalizing the well-known logistic
function is defined, and some of its basic properties studied. A simple formula
for the Lyapunov exponents of all the maps contained in this family is given
based on the construction of conjugacies. Moreover, it is shown that, despite
the dissimilarity of their polynomial expressions, all the maps possess the
same invariant density. Other algebraic properties of the family, which shows
some relationship with the set of Tschebysheff polynomials, are also
investigated.
