Constructions in elliptic dynamics

<span title="">2004</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="" style="color: black;">Ergodic Theory and Dynamical Systems</a> </i> &nbsp;
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
more &raquo; ... 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] .
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1017/s0143385703000798</a> <a target="_blank" rel="external noopener" href="">fatcat:pqsdttgpvvfqrksfs3jcwscz54</a> </span>
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