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

PhD Thesis

Habilitation Thesis

Selected talks