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Optimal transport and dynamics of expanding circle maps

Introductory Workshop on Optimal Transport: Geometry and Dynamics August 26, 2013 - August 30, 2013

August 29, 2013 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Benoît Kloeckner (Université de Grenoble I (Joseph Fourier))
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC


Abstract - Expanding circle maps are arguably the simplest examples of discrete-time dynamical systems on manifolds exhibiting a chaotic behavior. The goal of the talk will be to explain in this simple context how tools from optimal transport can shed new light on dynamical systems. More precisely, we will compute the derivative of the action on measures of an expanding circle map, at its absolutely continuous invariant measure, and study its spectral properties. Optimal transport is used to define the derivative, following the intuition of Otto and the framework of Gigli
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