Sarkovskii's Theorem

This chapter describes the entire range of dynamical behavior that can occur in a given dynamical system. It also describes the types of periodic behavior that can and cannot occur in a given system. Informally, the intermediate value theorem says that the mathematician can draw a continuous function without lifting our pencil from the paper. This intuition is important, but to understand and apply this theorem, they need a deeper and more formal understanding than the pencil analogy gives us. Sarkovskii's theorem provides a way of deducing the existence of different periodic orbits based on knowing the existence of a single periodic orbit.