Julia sets for Fibonacci endomorphisms of R~2

摘要

We study the dynamics of the family f_c(x,y) = (xy + c, x) of endomorphisms of R~2, where c is a real parameter. We investigate several topological properties of the forward and backward filled Julia sets. Then, through the study of adapted dynamical filtrations of the plane, we prove that for the interval of parameters given by 0 < c <(1/4), these two filled Julia sets can be described explicitly as finite unions of invariant manifolds.