Models for Dynamical Systems in Dimensions 1 and 2 - Lecture 2

Explore models for dynamical systems in dimensions 1 and 2 in this comprehensive lecture by André de Carvalho from Universidade de São Paulo. Delve into the renowned Milnor-Thurston theorem, which demonstrates that multimodal endomorphisms of the interval are semi-conjugate to piecewise linear maps with constant absolute slope (plcas). Examine how these models maintain the same topological entropy as the original endomorphisms. Investigate measurable pseudo-Anosov surface homeomorphisms as potential 2-dimensional analogs of plcas interval endomorphisms. Consider a conjectural extension of the Milnor-Thurston theorem for sufficiently smooth surface diffeomorphisms. Discover connections between this topic and Teichmüller Theory, as well as the geometry and topology of 3-manifolds. This 1 hour and 31 minute lecture, part of the Simons Semester on Dynamics, offers an in-depth exploration of advanced concepts in dynamical systems theory.