Title: Dynamics of laminations and foliations
Abstract:
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The main goal of this introductory course is to make the audience familiar with some aspects of the dynamics of laminations and holomorphic foliations by Riemann surfaces. The emphasis is on global dynamical properties of these objects. The central concepts are and leafwise Poincaré metric and directed positive harmonic currents. We develop the theory building on these concepts and using tools in Functional Analysis and Several Complex Variables. Our approach can be applied to the dynamical systems of more general laminations.
Nevertheless, we choose to show its effectiveness and to describe the theory for two large families of Riemann surface laminations: the laminations with singularities and the singular holomorphic foliations.
This course consists of three 1.5-hour-lectures accompanied by three 45-minute-exercise-sessions.Prerequisites to the course are standard Measure Theory and Integration, Function Theory of One Complex Variable, ODE, Differential Geometry and Functional Analysis. So fourth-year students can understand the course. How- ever, second-year students with a strong background are also welcome.
Keywords: Riemann surface lamination, singular holomorphic foliation, leafwise Poincaré metric, directed positive harmonic currents, harmonic measure, ergodic theorems.
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