On the non-integrability and dynamics of discrete models of threads

In the talk, we discuss the dynamics of planar n-gons, which can be considered as discrete models of threads. The main result is that, under some natural assumptions, these systems are not integrable in the sense of Liouville. This holds for both completely free threads and for threads with fixed points that are placed in external force fields. We also present sufficient conditions for the positivity of topological entropy in such systems. We briefly consider other dynamical properties of discrete threads and we also consider discrete models of inextensible yet compressible threads. The talk is based on a joint work with V.V. Kozlov.