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Partition sensitivity for measurable maps

C. A. Morales (2013)

Mathematica Bohemica

We study countable partitions for measurable maps on measure spaces such that, for every point x , the set of points with the same itinerary as that of x is negligible. We prove in nonatomic probability spaces that every strong generator (Parry, W., Aperiodic transformations and generators, J. London Math. Soc. 43 (1968), 191–194) satisfies this property (but not conversely). In addition, measurable maps carrying partitions with this property are aperiodic and their corresponding spaces are nonatomic....

Physical measures for infinite-modal maps

Vítor Araújo, Maria José Pacifico (2009)

Fundamenta Mathematicae

We analyze certain parametrized families of one-dimensional maps with infinitely many critical points from the measure-theoretical point of view. We prove that such families have absolutely continuous invariant probability measures for a positive Lebesgue measure subset of parameters. Moreover, we show that both the density of such a measure and its entropy vary continuously with the parameter. In addition, we obtain exponential rate of mixing for these measures and also show that they satisfy the...

Polynomial decay of correlations for a class of smooth flows on the two torus

Bassam Fayad (2001)

Bulletin de la Société Mathématique de France

Kočergin introduced in 1975 a class of smooth flows on the two torus that are mixing. When these flows have one fixed point, they can be viewed as special flows over an irrational rotation of the circle, with a ceiling function having a power-like singularity. Under a Diophantine condition on the rotation’s angle, we prove that the special flows actually have a t - η -speed of mixing, for some η > 0 .

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