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Explore the second lecture in a series on methods for studying abelian actions and centralizers in dynamical systems. Delve into the concept of smooth centralizers and their significance in non-generic situations, particularly within algebraic dynamical systems. Examine the relationship between large centralizers and algebraic systems, focusing on Anosov dynamics. Investigate the progression from local to global results in centralizer rigidity, and the extension of these concepts to partially hyperbolic systems. Gain insights into the fundamental structures and examples of abelian actions, building upon the introduction provided in the first lecture of this mini-course on dynamics.
