Publications

  1. K. Frączek, On resonant energy sets for Hamiltonian systems with reflections, preprint arXiv:2405.14464.
  2. K. Frączek, M. Kim, Solving the cohomological equation for locally hamiltonian flows, part II - global obstructions, preprint arXiv:2306.02340.
  3. K. Frączek, M. Kim, Solving the cohomological equation for locally hamiltonian flows, part I - local obstructions, Adv. Math. 446 (2024), 109668.
  4. K. Frączek, M. Kim, New phenomena in deviation of Birkhoff integrals for locally Hamiltonian flows, J. Reine Angew. Math. 807 (2024), 81-149.
  5. K. Frączek, C. Ulcigrai, On the asymptotic growth of Birkhoff integrals for locally Hamiltonian flows and ergodicity of their extensions, Comment. Math. Helv. 99 (2024), 231-354.
  6. K. Frączek, C. Ulcigrai, Ergodic and Spectral Theory of Area-Preserving Flows on Surfaces. In: Silva, C.E., Danilenko, A.I. (eds) Ergodic Theory. Encyclopedia of Complexity and Systems Science Series. Springer, New York, NY, 2023. https://doi.org/10.1007/978-1-0716-2388-6_775
  7. K. Frączek, V. Rom-Kedar, Non-uniform ergodic properties of Hamiltonian flows with impacts, Ergod. Th. & Dynam. Sys. 43 (2023), 190-252.
  8. K. Frączek, A. Kanigowski, M. Lemańczyk, Prime number theorem for regular Toeplitz subshifts, Ergod. Th. & Dynam. Sys. 42 (2022), 1446-1473.
  9. K. Frączek, Recurrence for smooth curves in the moduli space and application to the billiard flow on nibbled ellipses, Analysis & PDE 14-3 (2021), 793-821.
  10. J. Chaika, K. Frączek, A. Kanigowski, C. Ulcigrai, Singularity of the spectrum for smooth area-preserving flows in genus two and translation surfaces well approximated by cylinders, Commun. Math. Phys. 381 (2021), 1369-1407.
  11. P. Berk, K. Frączek, T. de la Rue, On typicality of translation flows which are disjoint with their inverse, J. Inst. Math. Jussieu 19 (2020), 1677-1737.
  12. K. Frączek, Ergodic properties of the ideal gas model for infinite billiards, Physica D 390 (2019), 9-14.
  13. L. Flaminio, K. Frączek, J. Kułaga-Przymus, M. Lemańczyk, Approximate orthogonality of powers for ergodic affine unipotent diffeomorphisms on nilmanifolds, Studia Math. 244 (2019), 43-97.
  14. K. Frączek, M. Schmoll, On ergodicity of foliations on $\Z^d$-covers of half-translation surfaces and some applications to periodic systems of Eaton lenses, Commun. Math. Phys. 362 (2018), 609-657.
  15. K. Frączek, P. Hubert, Recurrence and non-ergodicity in generalized wind-tree models, Math. Nachr. 291 (2018), 1686-1711.
  16. K. Frączek, R. Shi, C. Ulcigrai, Genericity on curves and applications: pseudo-integrable billiards, Eaton lenses and gap distributions, J. Mod. Dyn. 12 (2018), 55-122.
  17. K. Frączek, M. Lemańczyk, A class of mixing special flows over two-dimensional rotations, Discrete Contin. Dyn. Syst. 35 (2015), 4823-4829.
  18. P. Berk, K. Frączek, On special flows over IETs that are not isomorphic to their inverses, Discrete Contin. Dyn. Syst. 35 (2015), 829-855.
  19. K. Frączek, M. Schmoll, Directional localization of light rays in a periodic array of retro-reflector lenses, Nonlinearity 27 (2014), 1689-1707.
  20. K. Frączek, C. Ulcigrai, Non-ergodic Z-periodic billiards and infinite translation surfaces, Inventiones Math. 197 (2014), 241-298.
  21. K. Frączek, J. Kułaga, M. Lemańczyk, Non-reversibility and self-joinings of higher orders for ergodic flows, J. Anal. Math. 122 (2014), 163-227.
  22. K. Frączek, C. Ulcigrai, Ergodic directions for billiards in a strip with periodically located obstacles, Commun. Math. Phys. 327 (2014), 643-663.
  23. K. Frączek, A. Piękniewska, D. Skrenty, Mixing automorphisms which are Markov quasi-equivalent but not weakly isomorphic, Ergodic Theory and Dynamical Systems, Proceedings of the Ergodic Theory Workshops at University of North Carolina at Chapel Hill, 2011-2012, Edited by I. Assani, De Gruyter Proceedings in Mathematics, 2014, pages: 129-138.
  24. K. Frączek, J. Kułaga, M. Lemańczyk, On the self-similarity problem for Gaussian-Kronecker flows, Proc. Amer. Math. Soc. 141 (2013), 4275-4291.
  25. K. Frączek, C. Ulcigrai, Ergodic properties of infinite extensions of area-preserving flows, Math. Ann. 354 (2012), 1289-1367.
  26. J.-P. Conze, K. Frączek, Cocycles over interval exchange transformations and multivalued Hamiltonian flows, Adv. Math. 226 (2011), 4373-4428.
  27. K. Frączek, M. Lemańczyk, Ratner's property and mixing for special flows over two--dimensional rotations (extended version), this is an extended version of the paper published in J. Mod. Dyn. 4 (2010), 609-635.
  28. K. Frączek, M. Lemańczyk, A note on quasi-similarity of Koopman operators, J. London Math. Soc. (2) (2010) 82, 361-375.
  29. K. Frączek, M. Lemańczyk, On Hausdorff dimension of the set of closed orbits for a cylindrical transformation, Nonlinearity 23 (2010), 2393-2422.
  30. J. Brzykcy, K. Frączek, Disjointness of interval exchange transformations from systems of probabilistic origin, Discrete Contin. Dyn. Syst. 27 (2010), 53-73.
  31. K. Frączek, M. Lemańczyk, On the self-similarity problem for ergodic flows, Proc. London Math. Soc. 99 (2009), 658-696.
  32. K. Frączek, Density of mild mixing property for vertical flows of Abelian differentials, Proc. Amer. Math. Soc. 137 (2009), 4129-4142.
  33. K. Frączek, M. Lemańczyk, Smooth singular flows in dimension 2 with the minimal self-joining property, Monatsh. Math. 156 (2009), 11-45.
  34. K. Frączek, L. Polterovich, Growth and mixing, J. Mod. Dyn. 2 (2008), 315-338.
  35. K. Frączek, M. Wysokińska, Note on isomorphism problem for weighted unitary operators associated with a nonsingular automorphism , Colloq. Math. 110 (2008), 201-204.
  36. Y. Derriennic, K. Frączek, M. Lemańczyk, F. Parreau, Ergodic automorphisms whose weak closure of off-diagonal measures consists of ergodic self-joinings, Colloq. Math. 110 (2008), 81-115.
  37. K. Frączek, M. Lemańczyk, E. Lesigne, Mild mixing property for special flows under piecewise constant functions , Discrete Contin. Dyn. Syst. 19 (2007), 691-710.
  38. K. Frączek, M. Lemańczyk, On mild mixing of special flows over irrational rotations under piecewise smooth functions, Ergodic Theory Dynam. Systems 26 (2006), no.3, 719-738.
  39. K. Frączek, M. Lemańczyk, On disjointness properties of some smooth flows, Fund. Math. 185 (2005), No.2, 117-142
  40. K. Frączek, M. Lemańczyk, A class of special flows over irrational rotations which is disjoint from mixing flows, Ergodic Theory Dynam. Systems 24 (2004), no. 4, 1083-1095
  41. K. Frączek, On diffeomorphisms with polynomial growth of the derivative on surfaces, Colloq. Math. 99 (2004), no. 1, 75-90
  42. K. Frączek, Polynomial growth of the derivative for diffeomorphisms on tori, Discrete Contin. Dyn. Syst. 11 (2004), no. 2-3, 489-516
  43. K. Frączek, On the degree of cocycles with values in the group SU(2), Israel J. Math. 139 (2004), 293-317
  44. K. Frączek, M. Lemańczyk, On symmetric logarithm and some old examples in smooth ergodic theory, Fund. Math. 180 (2003), no. 3, 241-255
  45. K. Frączek, Measure-preserving diffeomorphisms of the torus, Ergodic Theory Dynam. Systems 21 (2001), no. 6, 1759-1781
  46. K. Frączek, Some examples of cocycles with simple continuous singular spectrum, Studia Math. 146 (2001), no. 1, 1-13
  47. K. Frączek, On cocycles with values in the group SU(2), Monatsh. Math. 131 (2000), no. 4, 279-307
  48. K. Frączek, Linear growth of the derivative for measure-preserving diffeomorphisms, Dedicated to the memory of Anzelm Iwanik. Colloq. Math. 84/85 (2000), part 1, 147-157
  49. K. Frączek, On ergodicity of some cylinder flows, Fund. Math. 163 (2000), no. 2, 117-130
  50. K. Frączek, Circle extensions of $Z\sp d$-rotations on the d-dimensional torus, J. London Math. Soc. (2) 61 (2000), no. 1, 139-162
  51. K. Frączek, Cyclic space isomorphism of unitary operators, Studia Math. 124 (1997), no. 3, 259-267
  52. K. Frączek, On a function that realizes the maximal spectral type, Studia Math. 124 (1997), no. 1, 1-7

Master Thesis

Spectral properties of cocycles over rotations , Nicolaus Copernicus University, Toruń 1995

PhD Thesis

Spectral properties of dynamical systems, Nicolaus Copernicus University, Toruń 1998 (in Polish)

Habilitation Thesis

Diffeomorphisms with polynomial growth of the derivative (selfreport), Nicolaus Copernicus University, Toruń 2005

Selected talks

  • Mildly mixing flows on surfaces, AMS-PTM Meeting, Warszawa 2007
  • Self-similarity for ergodic flows, ``Operator Theory and Applications: Perspectives and Challenges'', Jurata 2010
  • Recurrence and ergodicity of cocycles over IETs, ``Dynamical Systems Meeting, Lower Silesia 2010'', Trzebieszowice 2010