Milnor attractors and period incrementing on pattern iterations of flat top tent maps

In this paper, we consider the family of non-autonomous dynamical systems obtained by iterating tent maps with a flat top of constant value $u$ introduced at instants $i$ such that $s_i=0$, where $s$ is a binary sequence that we call the iteration pattern. We introduce symbolic dynamics and study the kneading invariants for these dynamical systems. More precisely, we define the kneading invariants $K(u,s)$ as symbolic sequences and study sufficient conditions for a symbolic sequence to be a kneading invariant $K(u,s)$ for some $u$, for each iteration pattern $s$. Finally, we describe the parameters $u$ for which there are Milnor attractors for iteration patterns $s$ such that $s_{np}=0$ for all $n$, as limits of parameter sequences corresponding to local attractors, organized according to a period-incrementing structure.