-
1Academic Journal
المؤلفون: Li, Jinjun, Wu, Min
مصطلحات موضوعية: keyword:irregular set, keyword:maximal Birkhoff average oscillation, keyword:specification property, keyword:residual set, msc:37C45, msc:54E52, msc:54H20
وصف الملف: application/pdf
Relation: mr:MR3483235; zbl:Zbl 06587886; reference:[1] Albeverio, S., Pratsiovytyi, M., Torbin, G.: Topological and fractal properties of real numbers which are not normal.Bull. Sci. Math. 129 (2005), 615-630. Zbl 1088.28003, MR 2166730, 10.1016/j.bulsci.2004.12.004; reference:[2] Baek, I.-S., Olsen, L.: Baire category and extremely non-normal points of invariant sets of IFS's.Discrete Contin. Dyn. Syst. 27 (2010), 935-943. Zbl 1234.11097, MR 2629566, 10.3934/dcds.2010.27.935; reference:[3] Barreira, L., Li, J., Valls, C.: Irregular sets are residual.Tohoku Math. J. (2) 66 (2014), 471-489. MR 3350279, 10.2748/tmj/1432229192; reference:[4] Barreira, L., Schmeling, J.: Sets of ``non-typical'' points have full topological entropy and full Hausdorff dimension.Isr. J. Math. 116 (2000), 29-70. MR 1759398, 10.1007/BF02773211; reference:[5] Bisbas, A., Snigireva, N.: Divergence points and normal numbers.Monatsh. Math. 166 (2012), 341-356. Zbl 1279.11079, MR 2925141, 10.1007/s00605-011-0289-1; reference:[6] Bowen, R.: Periodic points and measures for axiom A diffeomorphisms.Trans. Am. Math. Soc. 154 (1971), 377-397. MR 0282372; reference:[7] Buzzi, J.: Specification on the interval.Trans. Am. Math. Soc. 349 (1997), 2737-2754. MR 1407484, 10.1090/S0002-9947-97-01873-4; reference:[8] Ercai, C., Küpper, T., Lin, S.: Topological entropy for divergence points.Ergodic Theory Dyn. Syst. 25 (2005), 1173-1208. Zbl 1098.37013, MR 2158401; reference:[9] Denker, M., Grillenberger, C., Sigmund, K.: Ergodic Theory on Compact Spaces.Lecture Notes in Mathematics 527 Springer, Berlin (1976). MR 0457675; reference:[10] Fan, A.-H., Feng, D.-J.: On the distribution of long-term time averages on symbolic space.J. Stat. Phys. 99 (2000), 813-856. MR 1766907, 10.1023/A:1018643512559; reference:[11] Fan, A.-H., Feng, D.-J., Wu, J.: Recurrence, dimension and entropy.J. Lond. Math. Soc., (2) 64 (2001), 229-244. Zbl 1011.37003, MR 1840781, 10.1017/S0024610701002137; reference:[12] Fan, A., Liao, L., Peyri{è}re, J.: Generic points in systems of specification and Banach valued Birkhoff ergodic average.Discrete Contin. Dyn. Syst. 21 (2008), 1103-1128. Zbl 1153.37318, MR 2399452; reference:[13] Feng, D.-J., Lau, K.-S., Wu, J.: Ergodic limits on the conformal repellers.Adv. Math. 169 (2002), 58-91. Zbl 1033.37017, MR 1916371, 10.1006/aima.2001.2054; reference:[14] Hyde, J., Laschos, V., Olsen, L., Petrykiewicz, I., Shaw, A.: Iterated Cesàro averages, frequencies of digits, and Baire category.Acta Arith. 144 (2010), 287-293. Zbl 1226.11077, MR 2672291; reference:[15] Katok, A., Hasselblatt, B.: Introduction to the Modern Theory of Dynamical Systems.Encyclopedia of Mathematics and Its Applications 54 Cambridge Univ. Press, Cambridge (1995). Zbl 0878.58020, MR 1326374; reference:[16] Li, J., Li, B.: Hausdorff dimensions of some irregular sets associated with $\beta$-expansions.Sci. China Math. 59 (2016), 445-458. Zbl 1338.11076, MR 3457047, 10.1007/s11425-015-5046-9; reference:[17] Li, J., Wu, M.: A note on the rate of returns in random walks.Arch. Math. (Basel) 102 (2014), 493-500. Zbl 1296.54034, MR 3254792, 10.1007/s00013-014-0645-1; reference:[18] Li, J., Wu, M.: Generic property of irregular sets in systems satisfying the specification property.Discrete Contin. Dyn. Syst. 34 (2014), 635-645. Zbl 1280.54024, MR 3094597; reference:[19] Li, J., Wu, M.: Divergence points in systems satisfying the specification property.Discrete Contin. Dyn. Syst. 33 (2013), 905-920. Zbl 1271.37026, MR 2975141, 10.3934/dcds.2013.33.905; reference:[20] Li, J., Wu, M.: The sets of divergence points of self-similar measures are residual.J. Math. Anal. Appl. 404 (2013), 429-437. Zbl 1304.28008, MR 3045184, 10.1016/j.jmaa.2013.03.043; reference:[21] Li, J., Wu, M., Xiong, Y.: Hausdorff dimensions of the divergence points of self-similar measures with the open set condition.Nonlinearity 25 (2012), 93-105. Zbl 1236.28007, MR 2864378, 10.1088/0951-7715/25/1/93; reference:[22] Olsen, L.: Extremely non-normal numbers.Math. Proc. Camb. Philos. Soc. 137 (2004), 43-53. Zbl 1128.11038, MR 2075041, 10.1017/S0305004104007601; reference:[23] Olsen, L.: Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages.J. Math. Pures Appl. (9) 82 (2003), 1591-1649. Zbl 1035.37025, MR 2025314, 10.1016/j.matpur.2003.09.007; reference:[24] Olsen, L., Winter, S.: Normal and non-normal points of self-similar sets and divergence points of self-similar measures.J. Lond. Math. Soc., (2) 67 (2003), 103-122. Zbl 1040.28014, MR 1942414, 10.1112/S0024610702003630; reference:[25] Oxtoby, J. C.: Measure and Category. A Survey of the Analogies between Topological and Measure Spaces.Graduate Texts in Mathematics, Vol. 2 Springer, New York (1980). MR 0584443; reference:[26] Pitskel, B. S.: Topological pressure on noncompact sets.Funct. Anal. Appl. 22 (1988), 240-241 translation from Funkts. Anal. Prilozh. 22 (1988), 83-84. MR 0961770; reference:[27] Pollicott, M., Weiss, H.: Multifractal analysis of Lyapunov exponent for continued fraction and Manneville-Pomeau transformations and applications to Diophantine approximation.Commun. Math. Phys. 207 (1999), 145-171. MR 1724859, 10.1007/s002200050722; reference:[28] Ruelle, D.: Thermodynamic Formalism. The Mathematical Structures of Equilibrium Stastistical Mechanics.Cambridge Mathematical Library Cambridge University Press, Cambridge (2004). MR 2129258; reference:[29] Šalát, T.: A remark on normal numbers.Rev. Roum. Math. Pures Appl. 11 (1966), 53-56. MR 0201386; reference:[30] Sigmund, K.: On dynamical systems with the specification property.Trans. Am. Math. Soc. 190 (1974), 285-299. MR 0352411, 10.1090/S0002-9947-1974-0352411-X; reference:[31] Takens, F., Verbitskiy, E.: On the variational principle for the topological entropy of certain non-compact sets.Ergodic Theory Dyn. Syst. 23 (2003), 317-348. Zbl 1042.37020, MR 1971209; reference:[32] Thompson, D.: The irregular set for maps with the specification property has full topological pressure.Dyn. Syst. 25 (2010), 25-51. Zbl 1186.37034, MR 2765447, 10.1080/14689360903156237; reference:[33] Volkmann, B.: Gewinnmengen.Arch. Math. 10 German (1959), 235-240. MR 0105319
-
2Academic Journal
المؤلفون: Ganguly, D. K., Majumdar, M.
مصطلحات موضوعية: keyword:Baire category, keyword:property of Baire, keyword:residual set, keyword:upper semicontinuity, keyword:Borel set, msc:26A15, msc:26A21, msc:28A05
وصف الملف: application/pdf
Relation: mr:MR1658206; zbl:Zbl 0953.28001; reference:[1] R. Anantharaman and J.P. Lee: Planar sets whose complements do not contain a dense set of lines.Real Anal. Exch. 11 (1985–86), 168–178. MR 0828488, 10.2307/44151737; reference:[2] N.C. Bose Majumder: On some properties of sets with positive measures.Annali Dell’ Univ. di Ferrara (N.S.) Sez VII–Sci. Mat. X (1962), no. 1, 1–12.; reference:[3] J. Ceder and D.K. Ganguly: On projections of big planar sets.Real Anal. Exch. 9 (1983–84), 206–214. MR 0742785, 10.2307/44153528; reference:[4] D.K.Ganguly and S. Basu: On some properties of sets with positive measure.Czechoslovak Math. Jour. 44(119) (1994), 405–411. MR 1288161; reference:[5] Casper Goffman: Real Functions, Rinehart and Co.New York, 1953, p. 140. MR 0054006; reference:[6] T. Katkaniec: On category projections of cartesian product $A \times A$.Real Anal. Exch. 10 (1984–85), 233–234.; reference:[7] K. Kuratowski: Topology I.Academic Press, New York, 1966. MR 0217751; reference:[8] J.C. Oxtoby: Measure and Category, Second Edition.Springer-Verlag, 1980. MR 0584443; reference:[9] K.C. Ray: On some properties of ratio sets.Seminario mathematico dell Universita di Ferrara Ser VII (NS) 11 (1962–65), 45–49. MR 0188366; reference:[10] H. Steinhaus: Sur l’es distances des points des ensembles de measure positive.Fund. Math. 1 (1920), 93–104. MR 0023009, 10.4064/fm-1-1-93-104
-
3Academic Journal
المؤلفون: Neubrunová, A., Šalát, Tibor
مصطلحات موضوعية: keyword:Dirichlet function, keyword:almost continuity, keyword:cliquish function, keyword:residual set, keyword:transfinite sequence, keyword:almost quasicontinuity, keyword:types of convergence of sequences of almost quasicontinuous functions, keyword:quasicontinuity, msc:26A15, msc:54C05, msc:54C08, msc:54C30
وصف الملف: application/pdf
Relation: mr:MR1165897; zbl:Zbl 0756.26005; reference:[1] Borsík J., Doboš J.: On decomposition of quasicontinuity.Real Analysis Exchange 16 (1990-91), 292-305. MR 1087494, 10.2307/44153699; reference:[2] Doboš J.: Some generalizations of the notion of continuity and quasi-uniform conveгgence.Čas. pěst. mat. 106 (1981), 431-434. MR 0637824; reference:[3] Doboš J., Šalát T.: Cliquish functions, Riemann integrable functions and quasiuniform convergence.Acta Math. Univ. Comen. XL-XLl (1982), 219-223. MR 0686978; reference:[4] Fudali Lukasz A.: On cliquish functions on pгoduct spaces.Math. Slovaca 33 (1983), 53-58. MR 0689278; reference:[5] Husain T.: Almost continuous mappings.Prace matem. X (1966), 1-7. Zbl 0138.17601, MR 0220256; reference:[6] Kempisty S.: Sur les fonctions quasi-continues.Fund. Math. XIX (1932), 184-197. 10.4064/fm-19-1-184-197; reference:[7] Kuratowski K., Mostowski A.: Set Theoгy.PWN, Warszava, 1976.; reference:[8] Lipinski J. S., Šalát T.: On the points of quasicontinuity and cliquishness of functions.Czech. Math. J. 21 (1971), 484-489. Zbl 0219.26004, MR 0287517; reference:[9] Marcus S.: Sur les fonctions quasi-continues au sens de S. Kempisty.Coll. Math. VIII (1961), 47-53. MR 0125915; reference:[10] Matejdes M.: Applications of multifunctions in the theoгy of differentiation and integration.Thesis (1988). (In Slovak.); reference:[11] Neubrunová A.: On quasicontinuous and cliquish functions.Čas. pěst. mat. 99 (1974), 109-114. MR 0360948; reference:[12] Neubrunová A.: On transfinite sequences of certain types of functions.Acta F.R.N. Univ. Comen. 30 (1975), 121-125. MR 0385776; reference:[13] Sikorski R.: Real Functions I.PWN, Warszava, 1958. (In Polish.) MR 0091312; reference:[14] Šalát T.: Some generalizations of the notion of continuity and Denjoy propeгty of functions.Čas. pěst. mat. 99 (1974), 380-385. MR 0360947; reference:[15] Thielman H.: Types of functions.Amer. Math. Monthly 60 (1953), 156-161. Zbl 0051.13801, MR 0052495, 10.1080/00029890.1953.11988260; reference:[16] Wilhelm M.: Nearly lower semicontinuity and its applications.Pгoc. Fifth Praque Topol. Symp. (1981), 692-698. MR 0698476