Results 11 to 20 of about 5,030,646 (292)
From dual-unitary to quantum Bernoulli circuits: Role of the entangling power in constructing a quantum ergodic hierarchy [PDF]
Physical Review Research, 2021 Deterministic classical dynamical systems have an ergodic hierarchy, from ergodic through mixing, to Bernoulli systems that are “as random as a coin toss.” Dual-unitary circuits have been recently introduced as solvable models of many-body nonintegrable ...
S. Aravinda +2 more
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Slow Convergences of Ergodic Averages
Mathematical Notes, 2023 Birkhoff's theorem states that for an ergodic automorphism, the time averages converge to the space average. Given sequence $ψ(n)\to+0$, U. Krengel proved that for any ergodic automorphism there is an indicator such that the corresponding time averages converged a.e. with a rate slower than $ψ$. We prove again similar statements answering a question of
Валерий Валентинович Рыжиков +1 more
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Approximating the maximum ergodic average via periodic orbits [PDF]
Ergodic Theory and Dynamical Systems, 2008 Let sigma: Sigma(A) -> Sigma(A) be a subshift of finite type, let M-sigma be the set of all sigma-invariant Borel probability measures on Sigma(A), and let f : Sigma(A) -> R be a Holder continuous observable.
Contreras +3 more
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Impulse control maximising average cost per unit time: a non-uniformly ergodic case [PDF]
SIAM Journal of Control and Optimization, 2016 This paper studies maximisation of an average-cost-per-unit-time ergodic functional over impulse strategies controlling a Feller-Markov process. The uncontrolled process is assumed to be ergodic but, unlike the extant literature, the convergence to ...
Palczewski, Jan, Stettner, Lukasz
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Generic points in systems of specification and Banach valued Birkhoff ergodic average [PDF]
, 2008 We prove that systems satisfying the specification property are saturated in the sense that the topological entropy of the set of generic points of any invariant measure is equal to the measure-theoretic entropy of the measure.
Fan, Ai-Hua +2 more
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Convergence of diagonal ergodic averages [PDF]
Ergodic Theory and Dynamical Systems, 2009 AbstractTao has recently proved that ifT1,…,Tlare commuting, invertible, measure-preserving transformations on a dynamical system, then for anyL∞functionsf1,…,fl, the average (1/N)∑n=0N−1∏i≤lfi∘Tinconverges in theL2norm. Tao’s proof is unusual in that it translates the problem into a more complicated statement about the combinatorics of finite spaces ...
HENRY TOWSNER
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Multifractal analysis of multiple ergodic averages [PDF]
Comptes Rendus. Mathématique, 2011 In this Note we present a complete solution to the problem of multifractal analysis of multiple ergodic averages in the case of symbolic dynamics for functions of two variables depending on the first coordinate.
Aihua Fan, Jörg Schmeling, Meng Wu
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Pointwise convergence of some multiple ergodic averages [PDF]
, 2016 We show that for every ergodic system $(X,\mu,T_1,\ldots,T_d)$ with commuting transformations, the average \[\frac{1}{N^{d+1}} \sum_{0\leq n_1,\ldots,n_d \leq N-1} \sum_{0\leq n\leq N-1} f_1(T_1^n \prod_{j=1}^d T_j^{n_j}x)f_2(T_2^n \prod_{j=1}^d T_j^{n_j}
Sebastián Donoso, Wenbo Sun
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Learning Ergodic Averages in Chaotic Systems [PDF]
International Conference on Conceptual Structures, 2020 We propose a physics-informed machine learning method to predict the time average of a chaotic attractor. The method is based on the hybrid echo state network (hESN).
Francisco Huhn, L. Magri
semanticscholar +4 more sources
Convergence of polynomial ergodic averages [PDF]
Israel Journal of Mathematics, 2005 The main result of the paper is the proof of \(L^2\)-convergence of a product of measurable functions evaluated along polynomial times. Let \((X,{\mathcal B}, \mu,T)\) be an invertible dynamical system, let \(\{p_i(n)\}_{i=1}^\ell\) be integer polynomials, and let at least one of the following conditions hold: (i) the system \((X,{\mathcal B}, \mu,T)\)
Host, Bernard, Kra, Bryna
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