Title: Slow chaos: examples and mechanisms
Abstract: Many systems, from pure mathematics to physics, display a 'slow form' of the 'butterfly effect', a well popularized feature of chaotic systems. Examples span from dynamics (billiards in polygons and flows on surfaces), to geometry and algebra (the horocycle flow in hyperbolic geometry or Heisenberg nilflows), to mathematical physics (the Novikov or the Ehrenfest model).
While the mathematical theory of faster, more strongly chaotic systems (e.g. so called 'hyperbolic' dynamical sysems) is quite robust, 'slow chaos' is often display many 'nuances' and example-dependent features. Throughout these lectures we will explore some of the aspects of slow chaos, as well as some of the mechanisms and mathematical techniques that can be exploited to understand them ((from shearing, to renormalization, to the study of fluctuations and 'limit shapes').
In the first lecture we will introduce several examples of 'slowly chaotic' flows, as well as some examples of chaotic properties. We will then focus on the key mechanism of 'shearing' and some of its dynamical consequences.
Antonio Auffinger
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