Research interests: Dynamical Systems and Continuum Theory

My coauthors (in alphabetical order): Lluis Alseda (Universitat Autonoma de Barcelona), Adam Bartoš (Charles University in Prague), Alexander Blokh (Alabama University at Birmingham), Henk Bruin (University of Vienna),  Jernej Činč (University of Vienna and IT4Innovations University of Ostrava), Jan Dudák (Czech Technical University in Prague), Milan Kuchta (Slovak Academy of Sciences), Radek Marciňa (Charles University in Prague), Ivo Marek (Czech Technical University in Prague), Jan van Mill (University of Amsterdam), Michal Misiurewicz (Purdue University Indianapolis at Indianapolis), Zbigniew Nitecki (Tufts University in Boston), Piotr Oprocha (AGH University of Science and Technology and IT4Innovations University of Ostrava), Pavel Pyrih (Charles University in Prague), Samuel Roth (Silesian University in Opava), Lubomír Snoha (Matej Bel University in Banská Bystrica), Martin Soukenka (Czech Technical University in Prague), Serge Troubetzkoy (Aix Marseille Université), Benjamin Vejnar (Charles University in Prague), Ondřej Zindulka (Czech Technical University in Prague)

Organized conferences and seminars

 

Publications:

In preparation:

·         J. B., Kneading determinant of a unimodal map in two variables

·         J. B. (with H. Bruin), On solvability of M*v=lambda*v for lambda transient

·         J. B. (with M. Misiurewicz, Ľ. Snoha), Maximal Entropy Lebesgue measure

·         J. B. (with J. Činč, P. Oprocha, S. Troubetzkoy), The space of Lebesgue measure preserving maps is contractable

·         J. B. (with J. Činč, P. Oprocha, S. Troubetzkoy) Ergodic measures with infinite entropy

 

 

 

 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Submitted:

·         J. B. (with J. Činč, P. Oprocha, S. Troubetzkoy), Interval maps with dense periodicity, Submitted to Advances of Mathematics, June 2024,  29pp. C

·         J. B. (with J. Činč, P. Oprocha, S. Troubetzkoy), On Lebesgue measure preserving Besicovitch functions, submitted to Fundamenta Mathematicae, February 2026, 12pp.

 

 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Published:

           57. J. B., Corrigendum to 'On spaceability of Besicovitch functions', [C. R. Acad. Bulg.            

                  Sci. 68(8)(2015), 957--966], C. R. Acad. Bulg. Sci. 79(5)(2026), 557--560.

  56. J. B. (with J. Činč, P. Oprocha, S. Troubetzkoy), The generic continuous Lebesgue      

         measure preserving interval map is nowhere monotone but invertible a.e.,  

          to appear in Studia Mathematica, 2026, 16pp.

   55.   J. B. (with J. Dudák), Space of Besicovitch functions isometric to   

                    $\boldsymbol{c}$,  Bull. Belg. Math. Soc. Simon Stevin 33(2026), 138--144.

           54.   J. B. (with Ll. Alseda, M. Misiurewicz, Ľ. Snoha), The real teapot, Ergodic Th.    

                   and Dynamical Sys. 45(10)(2025), 2945—2975. C   

           53.   J. B. (with J. Činč, P. Oprocha, S. Troubetzkoy), Are generic dynamical  

                   properties stable under composition with rotations? Proceedings of A.M.S.    

                   152(7)(2024), 3011-3026. C

           52.   J. B. (with J. Činč, P. Oprocha, S. Troubetzkoy), Continuous Lebesgue   

                   measure preserving maps on one-dimensional manifolds: a survey, Topology 

                   Appl. 364(4)(2025), 109101. C

           51.   J. B. (with J. Činč, P. Oprocha, S. Troubetzkoy), S-limit shadowing is generic for   

       continuous Lebesgue measure preserving circle maps, Ergodic Theory and        

      Dynamical Systems 43(2023), 78-98. ISSN 0143-3857. C

           50.   J. B. (with S. Troubetzkoy), Topologically weakly mixing polygonal billiards,                       

                   Proc.Amer.Math.Soc. 151(8)(2023), 3391-3400, ISSN 0002-9939.

          49.  J. B. (with J. Činč, P. Oprocha, S. Troubetzkoy), Periodic points and shadowing 

                   for generic Lebesgue measure preserving interval maps,  Nonlinearity  

                   35(5)(2022), 2534-2557, ISSN 0951-7715. C

           48.  J. B. (with S. Troubetzkoy), Typical properties of  interval maps preserving  

                   the Lebesgue measure, Nonlinearity 33(12)(2020), 6461-6480,  

                  ISSN  0951-7715. C

.          47.  J. B. (with A. Bartoš, P. Pyrih, S. Roth, and B. Vejnar), Constant slope, entropy 

      and horseshoes for a map on a tame graph, Ergodic Th. and Dynamical Sys.

      40(11)(2020), 2970-2994, ISSN 0143-3857. C         

           46. J. B. (with A. Bartoš, van Mill, P. Pyrih and B. Vejnar), Compactifiable classes of     

                 compacta, Topology and its Applications 266(2019), 106836, ISSN 0166-8641. C                  

           45. J. B. (S. Roth), The infimum of Lipschitz constants in the conjugacy class of

                 an interval map, Proc.Amer.Math.Soc. 147(1)(2019), 255-269, ISSN 0002-9939. C

           44. J. B. (with P. Pyrih, B. Vejnar), On minimal homemorphisms on Peano continua,

                 Topology and its Applications 210 (2016), 263–268, ISSN 0166-8641.

           43. J. B. (with H. Bruin) Constant slope maps and the Vere-Jones classification, 

                 Entropy 18(6)(2016), doi:10.3390/e18060234, 27 pp., ISSN 1099-4300.

           42. J. B. (with P. Pyrih and B. Vejnar), Non-cut points, shore and non-block points in

                 continua, Glasnik Matematicki 51(1)(2016), 237-253, ISSN 0017-095X.    

41.  J. B. (with P. Pyrih and B. Vejnar), On blockers in continua, Topology and its Applications 202(2016), 346-355, ISSN 0166-8641.

40. J. B., On spaceability of Besicovitch functions, Comptes rendus de l'Académie 

      Bulgare des Sciences 68(8)(2015), 957-966, ISSN 1310–1331.

39.  J. B. (with S. Troubetzkoy), Homotopical rigidity of polygonal billiards, Topology and  its Applications 173(2014), 308-324, ISSN 0166-8641.

38.  J. B. (with R. Marciňa, P. Pyrih and B. Vejnar), Union of shore sets in a dendroid, Topology and  its Application 161(2014), 206-214, ISSN 0166-8641.

37. J. B. (with P. Pyrih and B. Vejnar), Half-homogeneous chainable continua with 

      end points, Topology and  its Applications 160 (2013), 1066-1073, ISSN 0166-

      8641. 

36. J. B., Semiconjugacy to a map of a constant slope, Studia Mathematica 208

      (2012), 213-228, ISSN 0039-3223.

35. J. B. (with S. Troubetzkoy), Code & Order in polygonal billiards, Topology

      and  its Applications 159 (2012), 236-247, ISSN 0166-8641.

34. J. B. (with H. Bruin), The topological entropy of Banach spaces, Journal of

      Difference Equations and Applications 18(4)(2012), 569-578, ISSN 1023-6198.

33. J. B. (with I. Marek), Monotony of solutions of some difference and differential

      equations, Lin. Alg. and its Appl. 436(10) (2012), 3919-3929, ISSN 0024-3795.

32. J. B. (with M. Soukenka), On piecewise affine interval maps with countably many

      laps, Discr. and Cont. Dynam. Sys.-A 31(3) (2011), 753-762, ISSN 1078-0947.

31. J. B. (with M. Soukenka), Irreducibility, infinite level sets and small entropy, Real

      Analysis Exchange 36(2) (2011), 449-462, ISSN 0147-1937.

30. J. B. (with S. Troubetzkoy), Does a billiard orbit determine its (polygonal) table?,                    

      Fundamenta Mathematicae 212 (2011), 129-144, ISSN 0016-2736.

29. J. B. (with A. Blokh), Asymptotic Behaviour of the Entropy of Interval Maps, \

      Journal of Differ. Eq. and Appl. 15(1) (2009), 1-11, ISSN 1023-6198.

28. J. B., Infinite dimensional Banach space of Besicovitch functions, Real Analysis

      Exchange 32(2007), 319-333, ISSN 0147-1937.

27. J. B. (with Z. Nitecki), Topological Entropy of m-fold Maps on Trees, Ergodic

      Theory and Dynamical Systems 27(2007), 671-701,ISSN 0143-3857.

26. J. B., On One-Parameter Families of Unimodal Maps, Collection of papers,

      Congratulations to K. Rektorys' birthday, 21-31.

25. J. B., On Multidimensional omega-Chaos, International Journal of Bifurcation and

      Chaos 16(3)(2006), 737-740, ISSN 0218-1274.

24. J. B., Forcing relation on interval patterns, Fundamenta Mathematicae 187 (2005),

      37-60, ISSN 0016-2736.

23. J. B., On a space of Besicovitch functions, Real Analysis Exchange

      30(1)(2004/2005), 173-182, ISSN 0147-1937.

22. J. B. (with Z. Nitecki), Topological Entropy of m-fold Maps, Ergodic Theory and

      Dynamical Systems 25(2)(2005), 375-401, ISSN 0143-3857.

21. J. B., The topological entropy versus level sets for interval maps (part II), Studia

      Mathematica 166(2005), 11-27, ISSN 0039-3223.

20. J. B., Strictly ergodic patterns and entropy for interval maps, Acta Math.

      Comenianae LXXII (1) (2003), 1-8, ISSN 0862-9544.

19. J. B., On Lipschitz extension of interval maps, Qualitative Theory of Dynamical

      Systems 4 (2) (2003), 17-30, ISSN 1575-5460.

18. J. B., Twist systems on the interval, Fundamenta Mathematicae 175(2) (2002), 97-

      117, ISSN 0016-2736.

17. J. B., The topological entropy versus level sets for interval maps Studia

      Mathematica 152(3) (2002), 249-261, ISSN 0039-3223.

16. J. B., Chaos in countable dynamical system, Topology and its Applications 126(1-

      2) (2002), 207-216, ISSN 0166-8641.

15. J. B. (with M. Kuchta), Irrational twist systems for interval maps, Real Analysis

      Exchange 27(2) (2001/2002), 441-456, ISSN 0147-1937.

14. J. B., On the topological entropy of green interval maps, Journal of Applied

      Analysis 7(2001), 107-112, ISSN 1425-6908.

13. J. B., Forcing relation on minimal interval patterns, Fundamenta Mathematicae

      169(2001), 161-173, ISSN 0016-2736.

12. J. B., A remark on topological entropy of unimodal Markov maps, Grazer Math.

      Ber. No.339(1999), 85-88, ISSN 1016-7692.

11. J. B., On entropy of patterns given by interval maps, Fundamenta Mathematicae

      162(1999), 1-36, ISSN 0016-2736.

10. J. B. (with O. Zindulka), On topological entropy on zero-dimensional compact

      spaces, Fund. Math. 162(1999), 233-249, ISSN 0016-2736.

09. J. B. (with M. Kuchta), X-minimal Patterns and Generalization of Sharkovskii's

      Theorem, Fund. Math. 156(1998), 33-66, ISSN 0016-2736.

08. J. B. (with M. Kuchta),  The X-minimal patterns and the forcing relation, Grazer

      Mathematischen Berichte. 334, 69-76.

07. J. B. (with M. Kuchta),  Register shifts versus transitive f-cycles for piecewise                    

      monotone maps,   Real Analysis Exchange 21(1)(1996), 134-146.

06. J. B. (with M. Kuchta),  Invar. measures for maps of the inter. that do not have                     

      points of some period, Erg. Th. and Dyn. Sys. 14(1)(1994), 9-21.

05. J. B., On isometric embeddings of Hilbert's cube into c,  Commentationes

      Mathematicae Universitatis Carolinae. 35(2)(1994), 361-364.

04. J. B., The functions with almost all points eventually periodic, Acta Mathematica

      Universitatis Comenianae 62(1)(1993), 123-134.

03. J. B. (with M. Kuchta), Topological entropy and variation for transitive maps,

      Mathematica Slovaca 43(3)(1993), 345-355.

02. J. B. (with L. Snoha), Periodic points and Little Fermat Theorem, Nieuw Archief

      voor Wiskunde 10(4)(1992), 33-35.

01.  J. B., On non-differentiable measure-preserving functions, Real Analysis

Exchange 16(1)(91), 119-129.