Periodic Orbits of Quadratic Polynomials of Periods Six and Seven

Abstract

The dynamics of quadratic polynomials is commonly studied by using the family of maps f c (x) = x 2 + c, where c ∈ C. In this paper we form equations of periodic orbits of periods six and seven on a new (u, v)-plane and consider also the corresponding equations on the (x, y)-plane. The new (u, v)-model produces equations for the periods six and seven with significantly lower degree than the ones obtained by the previous models which enables us to find their solutions.