Resumen de On a Non-conformal Cubic Family and Its Application

A.M. Alvez, D.S. Machado, P. Mehdipour, M. Salarinoghabi

• We consider a non-conformal cubic map given by Fc(z) = z3 + cz¯ for c real. We study some properties of filled Julia set of this map denoted by KFc and show that if |c| < 3/4 then KFc is connected. We also show that the map Fc(z) has relation not only to the cubic family fc(z) = z3+cz, but also to an important holomorphic map on complex projective space CP2 given by (z : w : η) → (z3 + cwη2 : w3 + czη2 : η3) with η = 0.