On the minimum ergodic average and minimal systems
نویسندگان
چکیده
We prove some equivalences associated with the case when average lower time is minimal. In addition, we characterize minimal systems by means of positivity invariant measures on open sets and also minimum ergodic averages. Finally, show that a system admits an set whose measure respect to its value can be chosen in [0, 1].
منابع مشابه
On the Average Length of Visits to an Ergodic Set
Let X1,X2, . . . be a sequence of random variables which are stationary and ergodic (see Breiman [1968, p. 109]) with values in a set S. Let μk be the stationary distribution for a sequence of length k so that for any fixed collection A1, A2, . . . , Ak of subsets of s, μk(A1, A2, . . . , Ak) = P[Xn ∈ A1,Xn+1 ∈ A2, . . . ,Xn+k−1 ∈ Ak] is independent of n, n = 1, 2, . . . . Now let B be a subset...
متن کاملDimension Spectrum for a Nonconventional Ergodic Average
We compute the dimension spectrum of certain nonconventional averages, namely, the Hausdorff dimension of the set of 0, 1 sequences, for which the frequency of the pattern 11 in positions k, 2k equals a given number θ ∈ [0, 1].
متن کاملMinimum Average Cost Clustering
A number of objective functions in clustering problems can be described with submodular functions. In this paper, we introduce the minimum average cost criterion, and show that the theory of intersecting submodular functions can be used for clustering with submodular objective functions. The proposed algorithm does not require the number of clusters in advance, and it will be determined by the ...
متن کاملMinimum Average Distance Triangulations
Some of the following problems look similar to the MAD Triangulation problem, but we have not found any deep connections: •Minimum Average Distance Spanning Subgraph in a budgeted version [2] was studied in the context of network design (minimizing average routing time). The problem is NP-complete even with unit weights. •Minimum Average Distance Spanning Tree [1]. NP-completeness is implied by...
متن کاملStationary policies for lower bounds on the minimum average cost of discrete-time nonlinear control systems
1Universidade Tecnológica Federal do Paraná, UTFPR, Av. Alberto Carazzai 1640, 86300-000 Cornelio Procópio-PR, Brazil. 2Basque Center for Applied Mathematics, BCAM, Alameda de Mazarredo 14, E-48009 Bilbao, Vizcaya, Spain. 3Universidade de Brası́lia, UnB, FT, Gleba A, SG11, 70910-900 Brası́lia-DF, Brazil. 4Universidade Estadual de Campinas, UNICAMP, FEEC-DT, Av. Albert Einstein 400, 13083-852 Camp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Cubo
سال: 2022
ISSN: ['0716-7776', '0719-0646']
DOI: https://doi.org/10.56754/0719-0646.2403.0457