منابع مشابه
Weakly Mixing Invariant Tori of Hamiltonian Systems
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We study the frequency of hypercyclicity of hypercyclic, non–weakly mixing linear operators. In particular, we show that on the space `(N), any sublinear frequency can be realized by a non–weakly mixing operator. A weaker but similar result is obtained for c0(N) or `(N), 1 < p <∞. Part of our results is related to some Sidon-type lacunarity properties for sequences of natural numbers.
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We show that Chacon's nonsingular type III transformation T , 0 < 1, is power weakly mixing, i.e., for all sequences of nonzero integers fk1; : : : ; krg, T k1 : : : T kr is ergodic. We then show that in in nite measure, this condition is not implied by in nite ergodic index (having all nite Cartesian products ergodic), and that in nite ergodic index does not imply 2-recurrence.
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At its inception in the early 1930’s, ergodic theory concerned itself with continuous one-parameter flows of measure preserving transformations ([Bi], [vN1], [KvN], [Ho1], [Ho2]). Soon it was realized that working with -actions rather than with -actions, has certain advantages. On the one hand, while the proofs become simpler, the results for -actions can often be easily derived from those for ...
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We describe a weakly mixing 1-dimensional tiling dynamical system in which the tiling space is modeled by a surface M of genus 2. The tiling system satis es an in ation, and the in ation map is modeled by a pseudo-Anosov di eomorphism D on M . The expansion coe cient for D is a non-Pisot number. In particular, the leaves of the expanding foliation for D are tiled by their visits to the elements...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 1987
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385700004090