Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

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Ergodic theory and its applications in dynamics, arithmetic, and algebra

2012/07/E/ST1/00185

Keywords:

ergodic theory Ramsey theory (infinite additive) combinatorics infinite products generalized Thue sequences sofic groups entropy quasifactors

Descriptors:

  • ST1_10: Ordinary differential equations and dynamical systems
  • ST1_3: Number theory
  • ST1_14: Discrete mathematics and combinatorics

Panel:

ST1 - Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution :

Uniwersytet Jagielloński w Krakowie, Wydział Matematyki i Informatyki

woj. małopolskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

dr hab. Dominik Kwietniak 

Number of co-investigators in the project: 6

Call: SONATA BIS 2 - announced on 2012-09-15

Amount awarded: 647 400 PLN

Project start date (Y-m-d): 2013-06-26

Project end date (Y-m-d): 2019-06-25

Project duration:: 72 months (the same as in the proposal)

Project status: Project settled

Information in the final report

  • Publication in academic press/journals (25)
  • Articles in post-conference publications (1)
  • Book publications / chapters in book publications (2)
  1. A note on the arithmetic properties of Stern polynomials
    Authors:
    M. Gawron
    Academic press:
    Publ. Math. Debrecen (rok: 2014, tom: 85, strony: 453-465), Wydawca: Published by the Institute of Mathematics, University of Debrecen, Hungary
    Status:
    Published
    DOI:
    10.5486/PMD.2014.6033 - link to the publication
  2. Arithmetic properties of coefficients of power series expansion of $\prod_{n=0}^{\infty}\left(1-x^{2^{n}}\right)^{t}$ (with an Appendix by Andrzej Schinzel)
    Authors:
    M. Gawron, P. Miska, M. Ulas
    Academic press:
    Monatsh. Math. (rok: 2018, tom: 185, strony: 307-360), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00605-017-1041-2 - link to the publication
  3. Automatic sequences and generalised polynomials
    Authors:
    J. Byszewski, J. Konieczny
    Academic press:
    Canadian Journal of Mathematics (rok: 2020, tom: 72, strony: 392-426), Wydawca: Canadian Mathematical Society
    Status:
    Published
    DOI:
    10.4153/S0008414X19000038 - link to the publication
  4. Combinatorial properties of Nil-Bohr sets
    Authors:
    J. Konieczny
    Academic press:
    Israel Journal of Mathematics (rok: 2017, tom: 220, strony: 333-385), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11856-017-1520-0 - link to the publication
  5. Factors of generalised polynomials and automatic sequences
    Authors:
    J. Byszewski, J. Konieczny
    Academic press:
    Indagationes Mathematicae (rok: 2018, tom: 29, strony: 981-985), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.indag.2018.03.003 - link to the publication
  6. Multi-recurrence and van der Waerden systems
    Authors:
    D. Kwietniak, J. Li, P. Oprocha, X. Ye
    Academic press:
    Sci. China Math. (rok: 2017, tom: 60, strony: 59–82), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11425-015-0860-8 - link to the publication
  7. On representing coordinates of points on elliptic curves by quadratic forms
    Authors:
    A. Bremner, M. Ulas
    Academic press:
    Acta Arithmetica (rok: 2017, tom: 179, strony: 55-78), Wydawca: Publications Department Institute of Mathematics Polish Academy of Sciences
    Status:
    Published
    DOI:
    10.4064/aa8597-1-2017 - link to the publication
  8. Points at rational distances from the vertices of certain geometric objects
    Authors:
    A. Bremner, M. Ulas
    Academic press:
    J. Number Theory (rok: 2016, tom: 158, strony: 104-133), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jnt.2015.06.011 - link to the publication
  9. Sparse generalised polynomials
    Authors:
    J. Byszewski, J. Konieczny
    Academic press:
    Trans. Amer. Math. Soc. (rok: 2018, tom: 370, strony: 8081-8109), Wydawca: AMS
    Status:
    Published
    DOI:
    10.1090/tran/7257 - link to the publication
  10. Two results on entropy, chaos, and independence in symbolic dynamics
    Authors:
    F. Falniowski, M. Kulczycki, D. Kwietniak, J. Li
    Academic press:
    Discrete and Continuous Dynamical Systems Series B (rok: 2015, tom: 20, strony: 3487 - 3505), Wydawca: AIMS
    Status:
    Published
    DOI:
    10.3934/dcdsb.2015.20.3487 - link to the publication
  11. On entropy of dynamical systems with almost specification
    Authors:
    D. Kwietniak, P. Oprocha, M. Rams
    Academic press:
    Israel Journal of Mathematics (rok: 2016, tom: 213, strony: 475–503), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11856-016-1339-0 - link to the publication
  12. Quasi-uniform Convergence in Dynamical Systems Generated by an Amenable Group Action
    Authors:
    Martha Łącka, Marta Straszak ( z d. Pietrzyk)
    Academic press:
    Journal of the London Mathematical Society (rok: 2018, tom: 98, strony: 687-707), Wydawca: London Mathematical Society
    Status:
    Published
    DOI:
    10.1112/jlms.12157 - link to the publication
  13. On Consecutive 1's in Continued Fractions Expansions of Square Roots of Prime Numbers
    Authors:
    P. Miska, M. ulas
    Academic press:
    Experimental Mathematics (rok: 2019, ), Wydawca: Taylor & Francis
    Status:
    Accepted for publication
    DOI:
    10.1080/10586458.2019.1605319 - link to the publication
  14. Arcwise connectedness of the set of ergodic measures of hereditary shifts
    Authors:
    J. Konieczny, M. Kupsa, D. Kwietniak
    Academic press:
    Proceedings of the American Mathematical Society (rok: 2018, tom: 146, strony: 3425-3438), Wydawca: AMS
    Status:
    Published
    DOI:
    10.1090/proc/14029 - link to the publication
  15. On $p$-adic valuations of colored $p$-ary partitions
    Authors:
    M Ulas, B. Żmija
    Academic press:
    Monatshefte für Mathematik (rok: 2019, tom: 188, strony: 351-368), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00605-018-1227-2 - link to the publication
  16. On formal inverse of the Prouhet-Thue-Morse sequence
    Authors:
    M. Gawron, M. Ulas
    Academic press:
    Discrete Math. (rok: 2016, tom: 339, strony: 1459-1470), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.disc.2015.12.016 - link to the publication
  17. Some experiments with Ramanujan-Nagell type Diophantine equations
    Authors:
    M. Ulas
    Academic press:
    Glas. Matematicki (rok: 2014, tom: 49, strony: 287-302), Wydawca: Croatian Mathematical Society and Department of Mathematics, University of Zagreb, Croatia
    Status:
    Published
    DOI:
    10.3336/gm.49.2.04 - link to the publication
  18. Rado's theorem for rings and modules
    Authors:
    J. Byszewski, E. Krawczyk
    Academic press:
    Journal of Combinatorial Theory Series A (rok: 2021, tom: 180, strony: 45319), Wydawca: Elsevier
    Status:
    Accepted for publication
    DOI:
    10.1016/j.jcta.2021.105402 - link to the publication
  19. Transitive dendrite map with zero entropy
    Authors:
    J. Byszewski, F. Falniowski, D. Kwietniak
    Academic press:
    Ergodic Theory and Dynamical Systems (rok: 2017, tom: 37, strony: 2077-2083), Wydawca: Cambridge University Press
    Status:
    Published
    DOI:
    10.1017/etds.2015.136 - link to the publication
  20. 2-adic valuations of coefficients of certain integer powers of formal power series
    Authors:
    M. Ulas
    Academic press:
    International Journal of Number Theory (rok: 2019, tom: 15, strony: 723-762), Wydawca: World Scientific
    Status:
    Published
    DOI:
    10.1142/S1793042119500386 - link to the publication
  21. On primitive integer solutions of the Diophantine equation t^2=G(x,y,z) and related results
    Authors:
    M. Gawron, M. Ulas
    Academic press:
    J. Number Theory (rok: 2016, tom: 159, strony: 101-122), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jnt.2015.07.012 - link to the publication
  22. Simultaneous $p$-oderings and minimising volumes in number fields
    Authors:
    J. Byszewski, M. Frączyk, A. Szumowicz
    Academic press:
    Journal of Number Theory (rok: 2017, tom: 173, strony: 478-511), Wydawca: Elsevier
    Status:
    Published
    DOI:
    0.1016/j.jnt.2016.09.010 - link to the publication
  23. Some identities involving Prouhet-Thue-Morse sequence and its relatives
    Authors:
    J. Byszewski, M. Ulas
    Academic press:
    Acta Mathematica Hungarica (rok: 2015, tom: 147, strony: 438-456), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10474-015-0547-0 - link to the publication
  24. Some observations concerning reducibility of quadrinomials
    Authors:
    A. Bremner, M. Ulas
    Academic press:
    Acta Mathematica Hungarica (rok: 2015, tom: 145, strony: 320-349), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10474-015-0478-9 - link to the publication
  25. Some properties of regular and rational sets
    Authors:
    Konrad Deka
    Academic press:
    Acta Arithmetica (rok: 2018, tom: 182, strony: 279-284), Wydawca: IM PAN
    Status:
    Published
    DOI:
    10.4064/aa170429-14-10 - link to the publication
  1. Some remarks about the Dedekind-Mertens lemma
    Authors:
    J. Byszewski
    Conference:
    Konferencja Algebra, Logic and Number Theory (ALANT 3) (rok: 2016, ), Wydawca: BANACH CENTER PUBLICATIONS vol. 108 (1) (2016)
    Data:
    konferencja 8-13 czerwca 2014
    Status:
    Published
  1. Sarnak's conjecture implies the Chowla conjecture along a subsequence
    Authors:
    A. Gomilko, D. Kwietniak, M. Lemańczyk
    Book:
    Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics (rok: 2018, tom: 2213, strony: 237-247), Wydawca: Springer
    Status:
    Published
  2. Mixing properties in coded systems
    Authors:
    J. Epperlein, D. Kwietniak, P. Oprocha
    Book:
    Pacifico M., Guarino P. (eds) New Trends in One-Dimensional Dynamics. Springer Proceedings in Mathematics & Statistics, vol 285. Springer, Cham. (rok: 2019, tom: 285, strony: 183-200), Wydawca: Springer / Springer Proceedings in Mathematics & Statistics
    Status:
    Published

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