PERIODIC ORBITS OF QUADRATIC POLYNOMIALS OF PERIODS SIX AND SEVEN

The dynamics of quadratic polynomials is commonly studied by using the family of maps $f_c (x) = x^2 + c$, where $c\in C$. 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.