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We study equidistribution properties of translations on nilmanifolds along functions of polynomial growth from a Hardy field. More precisely, if $X=G/Gamma$ is a nilmanifold, $a_1,ldots,a_kin G$ are commuting nilrotations, and $f_1,ldots,f_k$ are functions of polynomial growth from a Hardy field then we show that $bullet$ the distribution of the sequence $a_1^{f_1(n)}cdotldotscdot a_k^{f_k(n)}Gamma$ is governed by its projection onto the maximal factor torus, which extends Leibmans Equidistribution Criterion form polynomials to a much wider range of functions; and $bullet$ the orbit closure of $a_1^{f_1(n)}cdotldotscdot a_k^{f_k(n)}Gamma$ is always a finite union of sub-nilmanifolds, which extends some of the previous work of Leibman and Frantzikinakis on this topic.
Given Holder continuous functions $f$ and $psi$ on a sub-shift of finite type $Sigma_A^{+}$ such that $psi$ is not cohomologous to a constant, the classical large deviation principle holds (cite{OP}, cite{Kif}, cite{Y}) with a rate function $I_psigeq
We study mean convergence of multiple ergodic averages, where the iterates arise from smooth functions of polynomial growth that belong to a Hardy field. Our results include all logarithmico-exponential functions of polynomial growth, such as the fun
It is commonly assumed that a charged particle does not accelerate linearly along a spatially uniform magnetic field. We show that this is no longer the case if the interaction of the particle with the quantum vacuum is chiral, in which case parity a
We show that Sarnaks conjecture on Mobius disjointness holds in every uniquely ergodic modelof a quasi-discrete spectrum automorphism. A consequence of this result is that, for each non constant polynomial $PinR[x]$ with irrational leading coefficien
We present conditions that allow us to pass from the convergence of probability measures in distribution to the uniform convergence of the associated quantile functions. Under these conditions, one can in particular pass from the asymptotic distribut