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Session 16. Ergodic Theory and Dynamical Systems
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The Anosov-Katok method: educational remarks, history and new developments |
Roland Gunesch, PH Vorarlberg University of Education, Austria
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One of the main tools in Smooth Ergodic Theory is the method of
constructing \(C^\infty\)-diffeomorphisms with specified desired
properties by constructing a sequence of periodic maps. This method
allows to construct specific useful examples, which is very
important, since these are fundamentaly the main content in Smooth
Ergodic Theory. The method was invented by D. Anosov and A. B. Katok
and is currently seeing a revival. This talk explains the method and
its usefulness, gives and overview over the historical developments
of its application, and presents some entirely new results,
including novel constructions of weakly mixing diffeomorphisms with
desired extra properties.
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