Open Access

Besicovitch cascades and bounded partial quotients


Cite

D. V. Anosov, (1973), On an additive functional homology equation connected with an ergodic rotation of the circle, Math. USSR-Izv., 7:6, 1257 – 1271AnosovD. V.1973On an additive functional homology equation connected with an ergodic rotation of the circleMath. USSR-Izv.761257127110.1070/IM1973v007n06ABEH002086Search in Google Scholar

G. Atkinson, (1976), Recurrence of co-cycles and random walks, J. London Math. Soc., 13, 486–488.AtkinsonG.1976Recurrence of co-cycles and random walksJ. London Math. Soc.1348648810.1112/jlms/s2-13.3.486Search in Google Scholar

A.S. Besicovitch, (1937), A problem on topological transformation of the plane, Fund. Math., 28, 61–65.BesicovitchA.S.1937A problem on topological transformation of the planeFund. Math.28616510.4064/fm-28-1-61-65Search in Google Scholar

A.S. Besicovitch, (1951), A problem on topological transformations of the plane, Proc. Cambridge Philos. Soc., 47, 38–45.BesicovitchA.S.1951A problem on topological transformations of the planeProc. Cambridge Philos. Soc.47384510.4064/fm-28-1-61-65Search in Google Scholar

E. Dymek, (2013), Transitive cylinder flows whose set of discrete points is of full Hausdorff dimension, arXiv: 1303.3099v1 [math.DS], 13 mar 2013.DymekE.2013Transitive cylinder flows whose set of discrete points is of full Hausdorff dimensionarXiv: 1303.3099v1 [math.DS], 13 mar 2013.Search in Google Scholar

K. Falconer, (2003), Fractal geometry. Mathematical foundations and applications, John Wiley & Sons, Inc., Hoboken, NJ.FalconerK.2003Fractal geometry. Mathematical foundations and applicationsJohn Wiley & Sons, Inc.Hoboken, NJ10.1002/0470013850Search in Google Scholar

K. Frączek, M. Lemańczyk, (2010), On Hausdorff dimension of the set of closed orbits for a cylindrical transformation, Nonlinearity, 23, 2393–2422.FrączekK.LemańczykM.2010On Hausdorff dimension of the set of closed orbits for a cylindrical transformationNonlinearity232393242210.1088/0951-7715/23/10/003Search in Google Scholar

W.H. Gottschalk, G.A. Hedlund, (1955), Topological Dynamics, Amer. Math. Soc. Colloq. Publ. 36, Amer. Math. Soc., Providence, RI, 1–148.GottschalkW.H.HedlundG.A.1955Topological DynamicsAmer. Math. Soc. Colloq. Publ.36Amer. Math. Soc., Providence, RI,114810.1090/coll/036Search in Google Scholar

A. Ya. Khinchin. (1964), Continued fractions, The University of Chicago Press, Chicago – London (transl. from Russian).KhinchinA. Ya.1964Continued fractionsThe University of Chicago PressChicago – London(transl. from Russian).Search in Google Scholar

A. Kochergin, (2002), A mixing special flow over a circle rotation with almost Lipschitz function, Sbornik: Mathematics, 193, 359–385.KocherginA.2002A mixing special flow over a circle rotation with almost Lipschitz functionSbornik: Mathematics19335938510.1070/SM2002v193n03ABEH000636Search in Google Scholar

A. Kochergin, (2015), A Besicovitch Cylindrical Transformation with Hölder Function, Electronic Research Announcements in Mathematical Sciences, 22, 87 – 91. S 1935 – 9179 AIMS.KocherginA.2015A Besicovitch Cylindrical Transformation with Hölder FunctionElectronic Research Announcements in Mathematical Sciences228791S 1935 – 9179 AIMS.10.1134/S0001434616030068Search in Google Scholar

A. Kochergin, (2018), New examples of Besicovitch transitive cylindrical cascades, Sb. Math., 209:9, 1257–1272.KocherginA.2018New examples of Besicovitch transitive cylindrical cascadesSb. Math.20991257127210.1070/SM8936Search in Google Scholar

A. B. Krygin, (1975), An example of cylindrical cascade with anomalous metric properties, Vestn. Mosk. Univ., Ser. 1, Mat. Mekh., No. 5, 26–32.KryginA. B.1975An example of cylindrical cascade with anomalous metric propertiesVestn. Mosk. Univ., Ser. 1, Mat. Mekh.52632Search in Google Scholar

H. Poincaré, (1886), Sur les courbes défines par les équations différetielles (IV) (French), J. math. pures appl. 4 serie, 2, 151–218.PoincaréH.1886Sur les courbes défines par les équations différetielles (IV) (French)J. math. pures appl. 4 serie2151218Search in Google Scholar

V. V. Ryzhikov (1997), Polymorphisms, joinings, and the tensor simplicity of dynamical systems, Functional Analysis and Its Applications, 1997, 31:2, 109–118.RyzhikovV. V.1997Polymorphisms, joinings, and the tensor simplicity of dynamical systemsFunctional Analysis and Its Applications199731210911810.1007/BF02466016Search in Google Scholar

L.G. Schnirel’mann, (1930), An example of a plane transformation, Izv. Donskogo Politekhnich. Inst., 14, 64–74 (in Russian)Schnirel’mannL.G.1930An example of a plane transformationIzv. Donskogo Politekhnich. Inst.146474(in Russian)Search in Google Scholar

eISSN:
2444-8656
Language:
English
Publication timeframe:
Volume Open
Journal Subjects:
Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics