On a family of Self-Affine IFS whose attractors have a non-fractal top

Kevin G. Hare, Nikita Sidorov

Let $0<\lambda <\mu <1$ and $\lambda +\mu >1$. In this note we prove that for the vast majority of such parameters the top of the attractor $A_{\lambda ,\mu }$ of the IFS $\{(\lambda x,\mu y),(\mu x+1-\mu ,\lambda y+1-\lambda )\}$ is th…