On the Dynamics of the Family ax^d(x − 1) + x

In this paper we consider the dynamics of the real polynomials of degree d + 1 with a fixed point of multiplicity d ≥ 2. Such polynomials are conjugate to fa,d(x) = ax^d(x−1)+x, a ∈ R\{0}, d ∈ N. Our aim is to study the dynamics fa,d in some special cases.