Abstract
Using reparametrizations of linear flows, we show that there exist area-preserving real analytic maps of the three-dimensional torus that are ‘mixing of all orders’ and do not enjoy the monotone shrinking target property. Prior to that, we give a short proof of a result of Kurzweil from 1955: namely, that a translation Tα of the torus Td has the monotone shrinking target property if and only if the vector α is badly approximable (that is, of constant type). 2000 Mathematics Subject Classification 37E45, 37A25, 11J13. 2000 Mathematics Subject Classification 37E45, 37A25, 11J13.
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