Podvigin, I. V. On possible estimates of the rate of pointwise convergence in the Birkhoff ergodic theorem. (English. Russian original) Zbl 07505245 Sib. Math. J. 63, No. 2, 316-325 (2022); translation from Sib. Mat. Zh. 63, No. 2, 379-391 (2022). MSC: 37Axx 28Dxx 60Fxx PDF BibTeX XML Cite \textit{I. V. Podvigin}, Sib. Math. J. 63, No. 2, 316--325 (2022; Zbl 07505245); translation from Sib. Mat. Zh. 63, No. 2, 379--391 (2022) Full Text: DOI OpenURL
Tempelman, Arkady Randomized multivariate central limit theorems for ergodic homogeneous random fields. (English) Zbl 1479.60052 Stochastic Processes Appl. 143, 89-105 (2022). MSC: 60F05 60G10 37A30 PDF BibTeX XML Cite \textit{A. Tempelman}, Stochastic Processes Appl. 143, 89--105 (2022; Zbl 1479.60052) Full Text: DOI OpenURL
Hart, Allen G.; Hook, James L.; Dawes, Jonathan H. P. Echo state networks trained by Tikhonov least squares are \(L^2(\mu)\) approximators of ergodic dynamical systems. (English) Zbl 07477842 Physica D 421, Article ID 132882, 9 p. (2021). MSC: 37M25 37M10 PDF BibTeX XML Cite \textit{A. G. Hart} et al., Physica D 421, Article ID 132882, 9 p. (2021; Zbl 07477842) Full Text: DOI arXiv OpenURL
Ben-Artzi, Jonathan; Morisse, Baptiste Uniform convergence in von Neumann’s ergodic theorem in the absence of a spectral gap. (English) Zbl 07352594 Ergodic Theory Dyn. Syst. 41, No. 6, 1601-1611 (2021). MSC: 37A30 37A25 37A10 37C40 35Q41 35L05 PDF BibTeX XML Cite \textit{J. Ben-Artzi} and \textit{B. Morisse}, Ergodic Theory Dyn. Syst. 41, No. 6, 1601--1611 (2021; Zbl 07352594) Full Text: DOI arXiv Link OpenURL
Kachurovskii, A. G.; Podvigin, I. V.; Svishchev, A. A. The maximum pointwise rate of convergence in Birkhoff’s ergodic theorem. (English. Russian original) Zbl 1471.37005 J. Math. Sci., New York 255, No. 2, 119-123 (2021); translation from Zap. Nauchn. Semin. POMI 498, 18-25 (2020). Reviewer: Piotr Garbaczewski (Opole) MSC: 37A30 37A10 PDF BibTeX XML Cite \textit{A. G. Kachurovskii} et al., J. Math. Sci., New York 255, No. 2, 119--123 (2021; Zbl 1471.37005); translation from Zap. Nauchn. Semin. POMI 498, 18--25 (2020) Full Text: DOI OpenURL
Kachurovskiĭ, A. G.; Lapshtaev, M. N.; Khakimbaev, A. Dzh. Von Neumann’s ergodic theorem and Fejer sums for signed measures on the circle. (Russian. English summary) Zbl 1448.37004 Sib. Èlektron. Mat. Izv. 17, 1313-1321 (2020). MSC: 37A30 42A16 PDF BibTeX XML Cite \textit{A. G. Kachurovskiĭ} et al., Sib. Èlektron. Mat. Izv. 17, 1313--1321 (2020; Zbl 1448.37004) Full Text: DOI OpenURL
Bogachev, Vladimir I. Non-uniform Kozlov-Treschev averagings in the ergodic theorem. (English. Russian original) Zbl 07244020 Russ. Math. Surv. 75, No. 3, 393-425 (2020); translation from Usp. Mat. Nauk 75, No. 3, 3-36 (2020). MSC: 37A30 37A15 37A10 28D10 PDF BibTeX XML Cite \textit{V. I. Bogachev}, Russ. Math. Surv. 75, No. 3, 393--425 (2020; Zbl 07244020); translation from Usp. Mat. Nauk 75, No. 3, 3--36 (2020) Full Text: DOI OpenURL
Korda, Milan; Putinar, Mihai; Mezić, Igor Data-driven spectral analysis of the Koopman operator. (English) Zbl 1436.37093 Appl. Comput. Harmon. Anal. 48, No. 2, 599-629 (2020). MSC: 37M10 15B05 47N40 PDF BibTeX XML Cite \textit{M. Korda} et al., Appl. Comput. Harmon. Anal. 48, No. 2, 599--629 (2020; Zbl 1436.37093) Full Text: DOI arXiv OpenURL
Kachurovskii, A. G.; Podvigin, I. V. Measuring the rate of convergence in the Birkhoff ergodic theorem. (English. Russian original) Zbl 1427.37004 Math. Notes 106, No. 1, 52-62 (2019); translation from Mat. Zametki 106, No. 1, 40-52 (2019). MSC: 37A30 37A05 PDF BibTeX XML Cite \textit{A. G. Kachurovskii} and \textit{I. V. Podvigin}, Math. Notes 106, No. 1, 52--62 (2019; Zbl 1427.37004); translation from Mat. Zametki 106, No. 1, 40--52 (2019) Full Text: DOI OpenURL
Kachurovskii, A. G.; Podvigin, I. V. Fejér sums and Fourier coefficients of periodic measures. (English. Russian original) Zbl 1403.37016 Dokl. Math. 98, No. 2, 464-467 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 482, No. 4, 381-384 (2018). MSC: 37A45 42A16 PDF BibTeX XML Cite \textit{A. G. Kachurovskii} and \textit{I. V. Podvigin}, Dokl. Math. 98, No. 2, 464--467 (2018; Zbl 1403.37016); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 482, No. 4, 381--384 (2018) Full Text: DOI OpenURL
Kachurovskii, A. G.; Podvigin, I. V. Fejér sums for periodic measures and the von Neumann ergodic theorem. (English. Russian original) Zbl 1400.37009 Dokl. Math. 98, No. 1, 344-347 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 481, No. 4, 358-361 (2018). MSC: 37A30 PDF BibTeX XML Cite \textit{A. G. Kachurovskii} and \textit{I. V. Podvigin}, Dokl. Math. 98, No. 1, 344--347 (2018; Zbl 1400.37009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 481, No. 4, 358--361 (2018) Full Text: DOI OpenURL
Kachurovskii, A. G.; Knizhov, K. I. Deviations of Fejer sums and rates of convergence in the von Neumann ergodic theorem. (English. Russian original) Zbl 1400.37008 Dokl. Math. 97, No. 3, 211-214 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 480, No. 1, 21-24 (2018). MSC: 37A30 PDF BibTeX XML Cite \textit{A. G. Kachurovskii} and \textit{K. I. Knizhov}, Dokl. Math. 97, No. 3, 211--214 (2018; Zbl 1400.37008); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 480, No. 1, 21--24 (2018) Full Text: DOI OpenURL
Podvigin, I. V. Estimates for correlation in dynamical systems: from Hölder continuous functions to general observables. (Russian, English) Zbl 1413.37016 Mat. Tr. 20, No. 2, 90-119 (2017); translation in Sib. Adv. Math. 28, No. 3, 187-206 (2018). MSC: 37D20 37A50 60F10 PDF BibTeX XML Cite \textit{I. V. Podvigin}, Mat. Tr. 20, No. 2, 90--119 (2017; Zbl 1413.37016); translation in Sib. Adv. Math. 28, No. 3, 187--206 (2018) Full Text: DOI OpenURL
Kachurovskiĭ, A. G.; Podvigin, I. V. Large deviations of the ergodic averages: from Hölder continuity to continuity almost everywhere. (Russian, English) Zbl 1399.37001 Mat. Tr. 20, No. 1, 97-120 (2017); translation in Sib. Adv. Math. 28, No. 1, 23-38 (2018). MSC: 37A30 37A60 60F10 PDF BibTeX XML Cite \textit{A. G. Kachurovskiĭ} and \textit{I. V. Podvigin}, Mat. Tr. 20, No. 1, 97--120 (2017; Zbl 1399.37001); translation in Sib. Adv. Math. 28, No. 1, 23--38 (2018) Full Text: DOI OpenURL
Minabutdinov, A. R. Limiting curves for polynomial adic systems. (English. Russian original) Zbl 1379.37002 J. Math. Sci., New York 224, No. 2, 286-303 (2017); translation from Zap. Nauchn. Semin. POMI 448, 177-200 (2016). MSC: 37A05 37A30 37P05 PDF BibTeX XML Cite \textit{A. R. Minabutdinov}, J. Math. Sci., New York 224, No. 2, 286--303 (2017; Zbl 1379.37002); translation from Zap. Nauchn. Semin. POMI 448, 177--200 (2016) Full Text: DOI arXiv OpenURL
Fan, Aihua Almost everywhere convergence of ergodic series. (English) Zbl 1378.37011 Ergodic Theory Dyn. Syst. 37, No. 2, 490-511 (2017). Reviewer: Piotr Sworowski (Bydgoszcz) MSC: 37A30 28A20 26A27 PDF BibTeX XML Cite \textit{A. Fan}, Ergodic Theory Dyn. Syst. 37, No. 2, 490--511 (2017; Zbl 1378.37011) Full Text: DOI arXiv OpenURL
Kleinbock, Dmitry; Shi, Ronggang; Weiss, Barak Pointwise equidistribution with an error rate and with respect to unbounded functions. (English) Zbl 1417.37056 Math. Ann. 367, No. 1-2, 857-879 (2017). MSC: 37A45 37C85 37A50 28A33 22E40 37A17 PDF BibTeX XML Cite \textit{D. Kleinbock} et al., Math. Ann. 367, No. 1--2, 857--879 (2017; Zbl 1417.37056) Full Text: DOI arXiv OpenURL
Kachurovskii, Aleksandr G.; Podvigin, Ivan V. Estimates of the rate of convergence in the von Neumann and Birkhoff ergodic theorems. (English. Russian original) Zbl 1370.37014 Trans. Mosc. Math. Soc. 2016, 1-53 (2016); translation from Tr. Mosk. Mat. O.-va 77, No. 1, 1-66 (2016). Reviewer: Alejandro Mesón (La Plata) MSC: 37A30 37D20 37D50 60G10 PDF BibTeX XML Cite \textit{A. G. Kachurovskii} and \textit{I. V. Podvigin}, Trans. Mosc. Math. Soc. 2016, 1--53 (2016; Zbl 1370.37014); translation from Tr. Mosk. Mat. O.-va 77, No. 1, 1--66 (2016) Full Text: DOI OpenURL
Podvigin, I. V. On the rate of convergence in the individual ergodic theorem for the action of a semigroup. (Russian, English) Zbl 1374.37005 Mat. Tr. 18, No. 2, 93-111 (2015); translation in Sib. Adv. Math. 26, No. 2, 139-151 (2016). MSC: 37A30 37A50 37B50 PDF BibTeX XML Cite \textit{I. V. Podvigin}, Mat. Tr. 18, No. 2, 93--111 (2015; Zbl 1374.37005); translation in Sib. Adv. Math. 26, No. 2, 139--151 (2016) Full Text: DOI OpenURL
Chazottes, Jean-René Fluctuations of observables in dynamical systems: from limit theorems to concentration inequalities. (English) Zbl 1360.37017 González-Aguilar, Hernán (ed.) et al., Nonlinear dynamics new directions. Theoretical aspects. Cham: Springer (ISBN 978-3-319-09866-1/hbk; 978-3-319-09867-8/ebook). Nonlinear Systems and Complexity 11, 47-85 (2015). MSC: 37A45 37A30 37D25 60F05 60F10 37H10 PDF BibTeX XML Cite \textit{J.-R. Chazottes}, Nonlinear Syst. Complex. 11, 47--85 (2015; Zbl 1360.37017) Full Text: DOI arXiv OpenURL
Schweer, Sebastian; Wichelhaus, Cornelia Nonparametric estimation of the service time distribution in the discrete-time GI/G/\(\infty\) queue with partial information. (English) Zbl 1301.62037 Stochastic Processes Appl. 125, No. 1, 233-253 (2015). MSC: 62G05 60F17 60K25 PDF BibTeX XML Cite \textit{S. Schweer} and \textit{C. Wichelhaus}, Stochastic Processes Appl. 125, No. 1, 233--253 (2015; Zbl 1301.62037) Full Text: DOI arXiv OpenURL
Sedalishchev, V. V. Interrelation between the convergence rates in von Neumann’s and Birkhoff’s ergodic theorems. (English. Russian original) Zbl 1351.37031 Sib. Math. J. 55, No. 2, 336-348 (2014); translation from Sib. Mat. Zh. 55, No. 2, 412-426 (2014). MSC: 37A30 37A50 PDF BibTeX XML Cite \textit{V. V. Sedalishchev}, Sib. Math. J. 55, No. 2, 336--348 (2014; Zbl 1351.37031); translation from Sib. Mat. Zh. 55, No. 2, 412--426 (2014) Full Text: DOI OpenURL
Kachurovskii, A. G.; Podvigin, I. V. Large deviations and the rate of convergence in the Birkhoff ergodic theorem. (English. Russian original) Zbl 1370.37012 Math. Notes 94, No. 4, 524-531 (2013); translation from Mat. Zametki 94, No. 4, 569-577 (2013). Reviewer: Chryssoula Ganatsiou (Larissa) MSC: 37A30 28E05 PDF BibTeX XML Cite \textit{A. G. Kachurovskii} and \textit{I. V. Podvigin}, Math. Notes 94, No. 4, 524--531 (2013; Zbl 1370.37012); translation from Mat. Zametki 94, No. 4, 569--577 (2013) Full Text: DOI OpenURL
Kachurovskii, A. G.; Podvigin, I. V. Rates of convergence in ergodic theorems for certain billiards and Anosov diffeomorphisms. (English. Russian original) Zbl 1328.37005 Dokl. Math. 88, No. 1, 385-387 (2013); translation from Dokl. Akad. Nauk, 451, No. 1, 11-13 (2013). Reviewer: David Ralston (Westbury) MSC: 37A30 37D20 37A25 PDF BibTeX XML Cite \textit{A. G. Kachurovskii} and \textit{I. V. Podvigin}, Dokl. Math. 88, No. 1, 385--387 (2013; Zbl 1328.37005); translation from Dokl. Akad. Nauk, 451, No. 1, 11--13 (2013) Full Text: DOI OpenURL
Magalhães, M. L. S.; Pollicott, M. Geometry and dynamics of planar linkages. (English) Zbl 1260.55016 Commun. Math. Phys. 317, No. 3, 615-634 (2013). Reviewer: Michael Farber (Zürich) MSC: 55R80 53C99 PDF BibTeX XML Cite \textit{M. L. S. Magalhães} and \textit{M. Pollicott}, Commun. Math. Phys. 317, No. 3, 615--634 (2013; Zbl 1260.55016) Full Text: DOI Link OpenURL
Sedalishchev, V. V. Constants in the estimates of the convergence rate in the Birkhoff ergodic theorem with continuous time. (English. Russian original) Zbl 1260.37006 Sib. Math. J. 53, No. 5, 882-888 (2012); translation from Sib. Mat. Zh. 53, No. 5, 1102-1110 (2012). Reviewer: Makoto Mori (Tokyo) MSC: 37A30 37A10 PDF BibTeX XML Cite \textit{V. V. Sedalishchev}, Sib. Math. J. 53, No. 5, 882--888 (2012; Zbl 1260.37006); translation from Sib. Mat. Zh. 53, No. 5, 1102--1110 (2012) Full Text: DOI OpenURL
Shkredov, I. D. On the Pyatetskii-Shapiro normality criterion for continued fractions. (English. Russian original) Zbl 1297.11089 J. Math. Sci., New York 182, No. 4, 567-575 (2012); translation from Fundam. Prikl. Mat. 16, No. 6, 177-188 (2010). Reviewer: Chryssoula Ganatsiou (Larissa) MSC: 11K50 37A30 28D05 37A05 37B50 47A35 PDF BibTeX XML Cite \textit{I. D. Shkredov}, J. Math. Sci., New York 182, No. 4, 567--575 (2012; Zbl 1297.11089); translation from Fundam. Prikl. Mat. 16, No. 6, 177--188 (2010) Full Text: DOI OpenURL
Dzhulaĭ, N. A.; Kachurovskiĭ, A. G. Constants in the estimates of the rate of convergence in von Neumann’s ergodic theorem with continuous time. (English) Zbl 1285.47014 Sib. Math. J. 52, No. 5, 824-835 (2011); translation from Sib. Mat. Zh. 52, No. 5, 1039-1052 (2011). Reviewer: Jorge Miguel Milhazes de Freitas (Porto) MSC: 47A35 37A30 PDF BibTeX XML Cite \textit{N. A. Dzhulaĭ} and \textit{A. G. Kachurovskiĭ}, Sib. Math. J. 52, No. 5, 824--835 (2011; Zbl 1285.47014); translation from Sib. Mat. Zh. 52, No. 5, 1039--1052 (2011) Full Text: DOI OpenURL
Kachurovskii, A. G.; Sedalishchev, V. V. On the constants in the estimates of the rate of convergence in von Neumann’s ergodic theorem. (English. Russian original) Zbl 1273.47026 Math. Notes 87, No. 5, 720-727 (2010); translation from Mat. Zametki 87, No. 5, 756-763 (2010). MSC: 47A35 PDF BibTeX XML Cite \textit{A. G. Kachurovskii} and \textit{V. V. Sedalishchev}, Math. Notes 87, No. 5, 720--727 (2010; Zbl 1273.47026); translation from Mat. Zametki 87, No. 5, 756--763 (2010) Full Text: DOI OpenURL
Avigad, Jeremy; Gerhardy, Philipp; Towsner, Henry Local stability of ergodic averages. (English) Zbl 1187.37010 Trans. Am. Math. Soc. 362, No. 1, 261-288 (2010). Reviewer: Athanase Papadopoulos (Strasbourg) MSC: 37A30 03F60 03F03 PDF BibTeX XML Cite \textit{J. Avigad} et al., Trans. Am. Math. Soc. 362, No. 1, 261--288 (2010; Zbl 1187.37010) Full Text: DOI arXiv OpenURL
Brännström, Niklas Averaging in weakly coupled discrete dynamical systems. (English) Zbl 1191.37018 J. Nonlinear Math. Phys. 16, No. 4, 465-487 (2009). Reviewer: Jan Andres (Olomouc) MSC: 37D20 PDF BibTeX XML Cite \textit{N. Brännström}, J. Nonlinear Math. Phys. 16, No. 4, 465--487 (2009; Zbl 1191.37018) Full Text: DOI OpenURL
Cuny, Christophe; Lin, Michael Pointwise ergodic theorems with rate and application to the CLT for Markov chains. (English) Zbl 1186.37013 Ann. Inst. Henri Poincaré, Probab. Stat. 45, No. 3, 710-733 (2009). Reviewer: Cryssoula Ganatsiou (Larissa) MSC: 37A30 60F05 60J05 37A05 47A35 37A50 PDF BibTeX XML Cite \textit{C. Cuny} and \textit{M. Lin}, Ann. Inst. Henri Poincaré, Probab. Stat. 45, No. 3, 710--733 (2009; Zbl 1186.37013) Full Text: DOI EuDML OpenURL
Scott, Sherry E.; Redd, Thomas C.; Kuznetsov, Leonid; Mezić, Igor; Jones, Christopher K. R. T. Capturing deviation from ergodicity at different scales. (English) Zbl 1207.37005 Physica D 238, No. 16, 1668-1679 (2009). Reviewer: Dogan Çömez (Fargo) MSC: 37A05 28D05 37M25 PDF BibTeX XML Cite \textit{S. E. Scott} et al., Physica D 238, No. 16, 1668--1679 (2009; Zbl 1207.37005) Full Text: DOI OpenURL
Kachurovskii, A. G. General theories unifying ergodic averages and martingales. (English. Russian original) Zbl 1159.28005 Proc. Steklov Inst. Math. 256, 160-187 (2007); translation from Tr. Mat. Inst. Steklova 256, 172-200 (2007). Reviewer: Michael L. Blank (Moskva) MSC: 28D05 28D10 60G42 60G44 PDF BibTeX XML Cite \textit{A. G. Kachurovskii}, Proc. Steklov Inst. Math. 256, 160--187 (2007; Zbl 1159.28005); translation from Tr. Mat. Inst. Steklova 256, 172--200 (2007) Full Text: DOI OpenURL
Berkolaiko, G.; Keating, Jonathan P.; Smilansky, U. Quantum ergodicity for graphs related to interval maps. (English) Zbl 1122.81037 Commun. Math. Phys. 273, No. 1, 137-159 (2007). MSC: 81Q50 37A25 37E05 37N20 37E25 PDF BibTeX XML Cite \textit{G. Berkolaiko} et al., Commun. Math. Phys. 273, No. 1, 137--159 (2007; Zbl 1122.81037) Full Text: DOI arXiv OpenURL
Bardet, Jean-Baptiste; Gouëzel, Sébastien; Keller, Gerhard Limit theorems for coupled interval maps. (English) Zbl 1114.37006 Stoch. Dyn. 7, No. 1, 17-36 (2007). MSC: 37A30 37L60 60F05 37E05 PDF BibTeX XML Cite \textit{J.-B. Bardet} et al., Stoch. Dyn. 7, No. 1, 17--36 (2007; Zbl 1114.37006) Full Text: DOI arXiv OpenURL
Isola, Stefano Dispersion properties of ergodic translations. (English) Zbl 1130.37306 Int. J. Math. Math. Sci. 2006, No. 4, 20568, 20 p. (2006). MSC: 37A05 37E10 PDF BibTeX XML Cite \textit{S. Isola}, Int. J. Math. Math. Sci. 2006, No. 4, 20568, 20 p. (2006; Zbl 1130.37306) Full Text: DOI EuDML OpenURL
Bálint, Péter; Gouëzel, Sébastien Limit theorems in the stadium billiard. (English) Zbl 1170.37314 Commun. Math. Phys. 263, No. 2, 461-512 (2006). MSC: 37D50 37A60 PDF BibTeX XML Cite \textit{P. Bálint} and \textit{S. Gouëzel}, Commun. Math. Phys. 263, No. 2, 461--512 (2006; Zbl 1170.37314) Full Text: DOI arXiv OpenURL
Lopes, Artur O.; Lopes, Sílvia R. C. Convergence in distribution of the periodogram of chaotic processes. (English) Zbl 1007.62076 Stoch. Dyn. 2, No. 4, 609-624 (2002). MSC: 62M15 60F05 37A50 62M10 37A05 37M10 PDF BibTeX XML Cite \textit{A. O. Lopes} and \textit{S. R. C. Lopes}, Stoch. Dyn. 2, No. 4, 609--624 (2002; Zbl 1007.62076) Full Text: DOI OpenURL
Derriennic, Yves; Lin, Michael Fractional Poisson equations and ergodic theorems for fractional coboundaries. (English) Zbl 0988.47009 Isr. J. Math. 123, 93-130 (2001). Reviewer: Pavel Dyshlovenko (Ul’yanovsk) MSC: 47A35 28D05 37A30 47A60 PDF BibTeX XML Cite \textit{Y. Derriennic} and \textit{M. Lin}, Isr. J. Math. 123, 93--130 (2001; Zbl 0988.47009) Full Text: DOI OpenURL
Kachurovskii, A. G. On uniform convergence in the ergodic theorem. (English) Zbl 0936.28010 J. Math. Sci., New York 95, No. 5, 2546-2551 (1999). Reviewer: Michael L.Blank (Moskva) MSC: 28D05 37A30 PDF BibTeX XML Cite \textit{A. G. Kachurovskii}, J. Math. Sci., New York 95, No. 5, 2546--2551 (1999; Zbl 0936.28010) Full Text: DOI OpenURL
Gaposhkin, V. F. Decrease rate of the probabilities of \(\varepsilon\)-deviations for the means of stationary processes. (English. Russian original) Zbl 0930.60027 Math. Notes 64, No. 3, 316-321 (1998); translation from Mat. Zametki 64, No. 3, 366-372 (1998). Reviewer: Andrew Olenko (Kyïv) MSC: 60G10 PDF BibTeX XML Cite \textit{V. F. Gaposhkin}, Math. Notes 64, No. 3, 316--321 (1998; Zbl 0930.60027); translation from Mat. Zametki 64, No. 3, 366--372 (1998) Full Text: DOI OpenURL