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Constructions in elliptic dynamics
<span title="">2004</span>
<i title="Cambridge University Press (CUP)">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/t7qnh4dicrhptozut7w2ifbxua" style="color: black;">Ergodic Theory and Dynamical Systems</a>
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We present an overview and some new applications of the approximation by conjugation method introduced by Anosov and the second author more than thirty years ago [1]. Michel Herman made important contributions to the development and applications of this method beginning from the construction of minimal and uniquely ergodic diffeomorphisms jointly with Fathi in [7] and continuing with exotic invariant sets of rational maps of the Riemann sphere [21] , and the construction of invariant tori with
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... onstandard and unexpected behavior in the context of KAM theory [22, 23] . Recently the method has been experiencing a revival. Some of the new results presented in the paper illustrate variety of uses for tools available for a long time, others exploit new methods, in particular possibility of mixing in the context of Liouvillean dynamics discovered by the first author [8, 9] .
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