Voir la notice du chapitre de livre provenant de la source Math-Net.Ru
[1] A. M. Vershik, “Ravnomernaya algebraicheskaya approksimatsiya operatorov sdviga i umnozheniya”, DAN SSSR, 259:3 (1981), 526–529 | MR | Zbl
[2] A. M. Vershik, “Teorema o markovskoi periodicheskoi approksimatsii v ergodicheskoi teorii”, Zap. nauchn. sem. LOMI, 115, 1982, 72–82 | MR | Zbl
[3] A. M. Vershik, “Avtomorfizm Paskalya imeet nepreryvnyi spektr”, Funkts. analiz i ego pril., 453:3 (2011), 16–33 | MR
[4] M. I. Gordin, “O tsentralnoi predelnoi teoreme dlya statsionarnykh protsessov”, DAN SSSR, 188:4 (1969), 739–741 | MR | Zbl
[5] M. I. Gordin, “Zamechanie o martingalnom metode dokazatelstva tsentralnoi predelnoi teoremy dlya statsionarnykh posledovatelnostei”, Zap. nauchn. sem. POMI, 311, 2004, 124–132 | MR | Zbl
[6] A. A. Lodkin, I. E. Manaev, A. R. Minabutdinov, “Asimptotika masshtabirovannoi entropii avtomorfizma Paskalya”, Zap. nauchn. sem. POMI, 378, 2010, 58–72 | MR
[7] A. A. Lodkin, I. E. Manaev, A. R. Minabutdinov, “Realizatsiya avtomorfizma Paskalya v grafe konkatenatsii i funktsiya $s_2(n)$”, Zap. nauchn. sem. POMI, 403, 2012, 95–102 | MR
[8] A. P. Minabutdinov, I. E. Manaev, “Funktsiya Kruskala–Katony, posledovatelnost Konveya, krivaya Takagi i avtomorfizm Paskalya”, Zap. nauchn. sem. POMI, 411, 2013, 135–147
[9] A. P. Minabutdinov, “Sluchainye otkloneniya ergodicheskikh summ v avtomorfizme Paskalya dlya mery Lebega”, Zap. nauchn. sem. POMI, 432, 2015, 224–260 | Zbl
[10] A. P. Minabutdinov, “Asimptoticheskoe razlozhenie polinomov Kravchuka”, Zap. nauchn. sem. POMI, 436, 2015, 174–188
[11] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integraly i ryady, v. 3, Spetsialnye funktsii. Dopolnitelnye glavy, 2-e izdanie, Fizmatlit, 2003 | MR
[12] E. M. Rudo, “Asimptotika raspredelenii sluchainykh bluzhdanii na mnogomernykh grafakh Paskalya i na reshetkakh kornei”, Zap. nauchn. sem. POMI, 403, 2012, 158–171 | MR
[13] P. Allaart, K. Kawamura, “The Takagi function: a survey”, Real Anal. Exchange, 37:1 (2012), 1–54 | MR | Zbl
[14] L. Berg, M. Krüppel, “De Rham's singular function and related functions”, Z. Anal. Anwendungen, 19:1 (2000), 227–237 | DOI | MR | Zbl
[15] P. Billingsley, Probability and Measure, 3rd edition, Wiley, New York, 1995 | MR | Zbl
[16] E. de Amo, M. Diaz Carrillo, J. Fernandez-Sanchez, “Singular functions with applications to fractal dimensions and generalized Takagi functions”, Acta Appl. Math., 119:1 (2012), 129–148 | DOI | MR | Zbl
[17] E. de Amo, J. Fernandez-Sanchez, “A generalised dyadic representation system”, Int. J. Pure Appl. Math., 52:1 (2009), 49–66 | MR | Zbl
[18] G. de Rham, “Sur quelques courbes définies par des équations fonctionnelles”, Univ. e Politec. Torino. Rend. Sem. Mat., 16 (1956), 101–113 | MR
[19] R. Girgensohn, “Nowhere differentiable solutions of a system of functional equations”, Aequationes Math., 47:1 (1994), 89–99 | DOI | MR | Zbl
[20] R. Girgensohn, “Digital sums and functional equations”, Integers, 12:1 (2012), 141–160 | DOI | MR | Zbl
[21] A. Hajan, Y. Ito, S. Kakutani, “Invariant measure and orbits of dissipative transformations”, Adv. Math., 9:1 (1972), 52–65 | DOI | MR
[22] G. Halasz, “Remarks on the remainder in Birkhoff's ergodic theorem”, Acta Math. Acad. Sci. Hungar., 28:3–4 (1976), 389–395 | DOI | MR | Zbl
[23] É. Janvresse, T. de la Rue, “The Pascal adic transformation is loosely Bernoulli”, Ann. Inst. H. Poincaré Probab. Statist., 40:2 (2004), 133–139 | DOI | MR | Zbl
[24] É. Janvresse, T. de la Rue, Y. Velenik, “Self-similar corrections to the ergodic theorem for the Pascal-adic transformation”, Stoch. Dyn., 5:1 (2005), 1–25 | DOI | MR | Zbl
[25] S. Jukna, Extremal Combinatorics: With Applications in Computer Science, Springer, 2010 | MR
[26] S. Kakutani, “A problem of equidistribution on the unit interval $[0,1]$”, Lect. Notes Math., 541, 1976, 369–375 | DOI | MR | Zbl
[27] K. Kawamura, “On the set of points where Lebesgue's singular function has the derivative zero”, Proc. Japan Acad. Ser. A, 87:9 (2011), 162–166 | DOI | MR | Zbl
[28] M. Krawtchouk, “Sur une généralisation des polynômes d'Hermite”, C. R. Acad. Sci. Ser. Math., 189 (1929), 620–622 | Zbl
[29] M. Krüppel, “De Rham's singular function, its partial derivatives with respect to the parameter and binary digital sums”, Rostock. Math. Kolloq., 64 (2009), 57–74 | MR | Zbl
[30] M. Lacey, “On weak convergence in dynamical systems to self-similar processes with spectral representation”, Trans. Amer. Math. Soc., 328 (1991), 767–778 | DOI | MR | Zbl
[31] N. R. Ladhawala, “Absolute summability of Walsh–Fourier series”, Pacific J. Math., 65:1 (1976), 103–108 | DOI | MR | Zbl
[32] Z. Lomnicki, S. Ulam, “Sur la théorie de la mesure dans les espaces combinatoires et son application au calcul des probabilités. I. Variables indépendantes”, Fund. Math., 23 (1934), 237–278
[33] X. Mela, K. Petersen, “Dynamical properties of the Pascal adic transformation”, Ergodic Theory Dynam. Systems, 25:1 (2005), 227–256 | DOI | MR | Zbl
[34] T. Takagi, “A simple example of the continuous function without derivative”, Proc. Phys.-Math. Soc., 5–6 (1903), 176–177
[35] E. Trollope, “An explicit expression for binary digital sums”, Math. Mag., 41 (1968), 21–25 | DOI | MR | Zbl
[36] D. Volný, “Invariance principles and Gaussian approximation for strictly stationary processes.”, Trans. Amer. Math. Soc., 35:8 (1999), 3351–3371 | DOI | MR