Title: Slow chaos: low complexity and renormalization
Abstract: A feature of slowly chaotic systems is that they have 'low complexity' (in the sense that they can be encoded by sequences with many repetitive patterns, or more precisely, their 'entropy' is zero). An important technique to study many slowly chaotic systems is 'renormalization', which provides a tool to 'zoom' at different scales and uncover self-similarities. In this second (self-contained) lecture, we will provide an illustration of both phenomena through the example of 'cutting sequences' of linear trajectories in (regular) polygons. Affine symmetries and Veech groups can be used to 'renormalize' certain geometric structures on surfaces and provide a low-complexity ('a-dic') descriptions of these sequences. We will also hint at how less rigid forms of renormalization can explain 'approximately self-similar' objects, such as limit shapes and fluctuations of ergodic integrals.
Antonio Auffinger
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