Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

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Invariant measures, entropy and other parameters of growth in classical and non-classical dynamical systems

2013/08/A/ST1/00275

Keywords:

invariant measures entropy Lyapunov exponent sofic group action x2 x3 conjecture

Descriptors:

  • ST1_10: Ordinary differential equations and dynamical systems
  • ST1_13: Probability and statistics

Panel:

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

Host institution :

Instytut Matematyczny PAN

woj. mazowieckie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Tomasz Downarowicz 

Number of co-investigators in the project: 10

Call: MAESTRO 4 - announced on 2012-12-15

Amount awarded: 2 094 560 PLN

Project start date (Y-m-d): 2013-09-06

Project end date (Y-m-d): 2019-01-05

Project duration:: 64 months (the same as in the proposal)

Project status: Project settled

Information in the final report

  • Publication in academic press/journals (56)
  • Articles in post-conference publications (1)
  • Book publications / chapters in book publications (2)
  1. Almost sure convergence of the multiple ergodic average for certain weakly mixing systems
    Authors:
    Gutman, Y., Huang, W., Shao, S., & Ye, X
    Academic press:
    Acta Mathematica Sinica-English Ser. (rok: 2018, tom: 34, strony: 79-90), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10114-017-6366-1 - link to the publication
  2. Arcwise connectedness of the set of ergodic measures of hereditary shifts
    Authors:
    Jakub Konieczny, Michal Kupsa, Dominik Kwietniak
    Academic press:
    Proceedings of AMS (rok: 2018, tom: 146, strony: 3425-3438), Wydawca: American Mathematical Society
    Status:
    Published
    DOI:
    10.1090/proc/14029 - link to the publication
  3. Estimates for principal Lyapunov exponents: A survey
    Authors:
    Janusz Mierczyński
    Academic press:
    Nonautonomous Dynamical Systems (rok: 2014, tom: 1(1), strony: 137-162), Wydawca: De Gruyter
    Status:
    Published
    DOI:
    10.2478/msds-2014-0008 - link to the publication
  4. Isomorphic extensions and applications
    Authors:
    T. Downarowicz and Eli Glasner
    Academic press:
    Topological Methods in Nonlinear Analysis (rok: 2016, tom: 48, strony: 321-328), Wydawca: Juliusz Schauder Center for Nonlinear Studies
    Status:
    Published
    DOI:
    10.12775/TMNA.2016.050 - link to the publication
  5. Minimal spaces with cyclic group of homeomorphisms
    Authors:
    Tomasz Downarowicz, L'ubomir Snoha i Dariusz Tywoniuk
    Academic press:
    Journal of Dynamics and Differential Equations (rok: 2017, tom: 29, strony: 243–257), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10884-015-9433-2 - link to the publication
  6. Principal Floquet subspaces and exponential separations of type II with applications to random delay differential equations
    Authors:
    Janusz Mierczyński, Sylvia Novo, Rafael Obaya
    Academic press:
    Discrete and Continuous Dynamical Systems- series A (rok: 2018, tom: 38, strony: 6163-6193), Wydawca: American Institute of Mathematical Statistics
    Status:
    Published
    DOI:
    10.3934/dcds.2018265 - link to the publication
  7. Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. III. Parabolic equations and delay systems
    Authors:
    Janusz Mierczyński and Wenxian Shen
    Academic press:
    Journal of Dynamics and Differential Equations (rok: 2016, tom: 28, strony: 1039-1079), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10884-015-9436-z - link to the publication
  8. Universal systems for entropy intervals
    Authors:
    Tomasz Downarowicz i Jacek Serafin
    Academic press:
    Journal of Dynamics and Differential Equations (rok: 2017, tom: 29, strony: 1411-1422), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10884-015-9516-0 - link to the publication
  9. A Lipschitz Refinement of the Bebutov–Kakutani Dynamical Embedding Theorem
    Authors:
    Gutman, Y., Jin, L. & Tsukamoto, M.
    Academic press:
    Journal of Dynamics and Differential Equations (rok: 2018, tom: first view, strony: online), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10884-018-9653-3 - link to the publication
  10. A fresh look at the notion of normality
    Authors:
    Vitaly Bergelson, Tomasz Downarowicz and Michał Misiurewicz
    Academic press:
    Annali della Scuola normale superiore di Pisa, Classe di Scienze (rok: 2020, tom: 21, strony: 27-88), Wydawca: Scuola Normale Superiore
    Status:
    Published
    DOI:
    10.2422/2036-2145.201808_005 - link to the publication
  11. Decisive Bratteli-Vershik Models
    Authors:
    T. Downarowicz i O. Karpel
    Academic press:
    Studia Mathematica (rok: 2019, tom: 247, strony: 251-271), Wydawca: IMPAN
    Status:
    Published
    DOI:
    10.4064/sm170519-5-2 - link to the publication
  12. Empirical approach to the x2, x3 conjecture
    Authors:
    Tomasz Downarowicz, Dawid Huczek
    Academic press:
    Experimental Mathematics (rok: 2019, tom: online, strony: 45308), Wydawca: Taylor & Francis Online
    Status:
    Published
    DOI:
    10.1080/10586458.2019.1608603 - link to the publication
  13. Exact number of ergodic measures for Bratteli diagrams
    Authors:
    S. Bezuglyi, O. Karpel and J. Kwiatkowski
    Academic press:
    Journal of Mathematical Analysis and Applications (rok: 2019, tom: 480, strony: 17899), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2019.123431 - link to the publication
  14. Faces of simplices of invariant measures for group actions
    Authors:
    Bartosz Frej i Dawid Huczek
    Academic press:
    Monatshefte für Mathematik (rok: 2018, tom: 185, strony: 61-80), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00605-017-1116-0 - link to the publication
  15. The structure theory of Nilspaces II: Representation as nilmanifolds
    Authors:
    Yonatan Gutman, Freddie Manners and Péter Varjú
    Academic press:
    Transactions of the American Mathematical Society (rok: 2018, tom: online first, strony: 16803), Wydawca: AMS
    Status:
    Published
    DOI:
    10.1090/tran/7503 - link to the publication
  16. Robust existence of nonhyperbolic ergodic measures with positive entropy and full support
    Authors:
    Christian Bonatti, Lorenzo J. Díaz, Dominik Kwietniak
    Academic press:
    Annales scientifiques de l'École normale supérieure de Paris (), Wydawca: Société mathématique de France
    Status:
    Accepted for publication
    DOI:
    10.2422/2036-2145.202001_014 - link to the publication
  17. A note on the complexity function and entropy of pseudogroups
    Authors:
    D. Kwietniak i M. Łącka
    Academic press:
    Journal of Mathematical Analysis and Applications (rok: 2016, tom: 48, strony: 523-532), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2016.02.021 - link to the publication
  18. A panorama of specification-like properties and their consequences
    Authors:
    Dominik Kwietniak, Martha Łącka I Piotr Oprocha
    Academic press:
    Contemporary Mathematics (rok: 2016, tom: 669, strony: 155-186), Wydawca: American Mathematical Society
    Status:
    Published
    DOI:
    10.1090/conm/669 - link to the publication
  19. Application of signal analysis to the embedding problem of Zk-actions
    Authors:
    Yonatan Gutman, Yixiao Qiao and Masaki Tsukamoto
    Academic press:
    Geometric and Functional Analysis (rok: 2019, tom: 29, strony: 1440-1502), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00039-019-00499-z - link to the publication
  20. Entropy of subordinate shift spaces
    Authors:
    M. Kulczycki, D. Kwietniak and J. Li
    Academic press:
    American Mathematical Monthly (rok: 2018, tom: 125, strony: 141--148), Wydawca: Mathematical Association of America
    Status:
    Published
    DOI:
    10.1080/00029890.2018.1401875 - link to the publication
  21. Exploding Markov Operators
    Authors:
    Bartosz Frej
    Academic press:
    Positivity (rok: 2020, tom: 24, strony: 1435-1447), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11117-020-00739-9 - link to the publication
  22. Instability in linear cooperative systems of ordinary differential equations
    Authors:
    Janusz Mierczyński
    Academic press:
    SIAM Review (rok: 2017, tom: 59, strony: 649 – 670), Wydawca: Society for Industrial and Applied Mathematics
    Status:
    Published
    DOI:
    10.1137/141001147 - link to the publication
  23. The embedding problem in topological dynamics and Takens' theorem
    Authors:
    Yonatan Gutman, Yixiao Qiao and Gábor Szabó
    Academic press:
    Nonlinearity (rok: 2018, tom: 31, strony: 597), Wydawca: IOP Science
    Status:
    Published
    DOI:
    10.1088/1361-6544/aa9464 - link to the publication
  24. Tilings of amenable groups
    Authors:
    Tomasz Downarowicz, Dawid Huczek i Guohua Zhang
    Academic press:
    Journal fur die Reine und Angewandte Mathematik (rok: 2019, tom: 2019, strony: 277-298), Wydawca: De Gruyter
    Status:
    Published
    DOI:
    10.1515/ - link to the publication
  25. Topological entropy, upper Carathéodory capacity and fractal dimensions of semigroup actions
    Authors:
    Andrzej Biś, Dikran Dikranjan, Anna Giordano Bruno and Luchezar Stoyanov
    Academic press:
    Coll. Math. (rok: 2021, tom: 163, strony: 131-151), Wydawca: IMPAN
    Status:
    Published
    DOI:
    10.4064/cm8017-12-2019 - link to the publication
  26. An explicit compact universal space for real flows
    Authors:
    Yonatan Gutman i Lei Jin
    Academic press:
    Journal of Differential Equations (rok: 2019, tom: 266, strony: 3438-3449), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2018.09.007 - link to the publication
  27. Borel complexity of sets of normal numbers via generic points in subshifts with specification
    Authors:
    Dominik Kwietniak, Dylan Airey, Steve Jackson i Bill Mance
    Academic press:
    Transactions AMS (rok: 2020, tom: 373, strony: 4561-4584), Wydawca: AMS
    Status:
    Published
    DOI:
    10.1090/tran/8001 - link to the publication
  28. Extensions of Full Shifts with Group Actions
    Authors:
    Dawid Huczek i Bartosz Frej
    Academic press:
    Coll. Math. (rok: 2020, tom: 160, strony: 65-70), Wydawca: IMPAN
    Status:
    Published
    DOI:
    10.4064/cm7843-3-2019 - link to the publication
  29. Mean Dimension & Jaworski-type Theorems
    Authors:
    Yonatan Gutman
    Academic press:
    Proceedings of the London Mathematical Society (rok: 2015, tom: 111, strony: 831-850), Wydawca: Oxford Journals
    Status:
    Published
    DOI:
    10.1112/plms/pdv043 - link to the publication
  30. Mean dimension of Z^k -actions
    Authors:
    Yonatan Gutman, Elon Lindenstrauss i Masaki Tsukamoto
    Academic press:
    Geometric and Functional Analysis (rok: 2016, tom: 26, strony: 778-817), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00039-016-0372-9 - link to the publication
  31. Odometers and Toeplitz systems revisited in the context of Sarnak's conjecture
    Authors:
    Tomasz Downarowicz and Stanislaw Kasjan
    Academic press:
    Studia Mathematica (rok: 2015, tom: 229, strony: 45–72), Wydawca: The Hebrew University Magnes Pres
    Status:
    Published
    DOI:
    10.4064/sm8314-12-2015 - link to the publication
  32. Some remarks on dynamical systems of solenoids
    Authors:
    Andrzej Biś i W. Kozłowski
    Academic press:
    Taiwaneese Journal of Mathematics (rok: 2018, tom: 22, strony: 1463-1478), Wydawca: The Mathematical Society of the Republic of China
    Status:
    Published
    DOI:
    10.11650/tjm/180506 - link to the publication
  33. The C1 property of convex carrying simplices for competitive maps
    Authors:
    Janusz Mierczyński
    Academic press:
    Ergodic Theory and Dynamical Systems (rok: 2018, tom: online, strony: 45307), Wydawca: Cambridge University Press
    Status:
    Published
    DOI:
    10.1017/etds.2018.85 - link to the publication
  34. Topological entropy and homogeneous measure for a solenoid
    Authors:
    A. Biś, A. Namiecińska
    Academic press:
    Bulletin da la Societe des Sciences et des Lettres de Łódź (rok: 2017, tom: 67, strony: 21-32), Wydawca: Łódzkie Towarzystwo Naukowe
    Status:
    Published
    DOI:
    10.26485/0459-6854/2017/67.3/2 - link to the publication
  35. Zero-dimensional extensions of amenable group actions
    Authors:
    Dawid Huczek
    Academic press:
    Studia Mathematica (rok: 2021, tom: 256, strony: 121-145), Wydawca: IMPAN
    Status:
    Published
    DOI:
    10.4064/sm190203-5-11 - link to the publication
  36. A comment on ergodic theorem for amenable groups
    Authors:
    Bartosz Frej i Dawid Huczek
    Academic press:
    Canadian Mathematical Bulletin (rok: 2020, tom: 63, strony: 257-261), Wydawca: Canadian Mathematical Society
    Status:
    Published
    DOI:
    10.4153/S0008439519000110 - link to the publication
  37. A strictly ergodic, positive entropy subshift uniformly uncorrelated to the Mobius function
    Authors:
    Tomasz Downarowicz i Jacek Serafin
    Academic press:
    Studia Math (rok: 2020, tom: 251, strony: 195-206), Wydawca: IMPAN
    Status:
    Published
    DOI:
    10.4064/sm180719-13-12 - link to the publication
  38. Almost full entropy subshifts uncorrelated to the Möbius function
    Authors:
    Tomasz Downarowicz i Jacek Serafin
    Academic press:
    International Mathematics Research Notices (rok: 2017, tom: online, strony: 45305), Wydawca: Oxford Academic
    Status:
    Published
    DOI:
    10.1093/imrn/rnx192 - link to the publication
  39. Correlation of sequences and of measures, generic points for joinings and ergodicity of certain cocycles
    Authors:
    Jean-Pierre Conze, Tomasz Downarowicz and Jacek Serafin
    Academic press:
    Transactions of AMS (rok: 2017, tom: 369, strony: 3421-3441), Wydawca: American Mathematical Society
    Status:
    Published
    DOI:
    10.1090/tran/6788 - link to the publication
  40. Doubly stochastic operators with zero entropy
    Authors:
    Bartosz Frej i Dawid Huczek
    Academic press:
    Annals of Functional Analysis (rok: 2019, tom: 10, strony: 144-156), Wydawca: Duke University Press
    Status:
    Published
    DOI:
    10.1215/20088752-2018-0015 - link to the publication
  41. Dynamical quasitilings of amenable groups
    Authors:
    T. Downarowicz i D. Huczek
    Academic press:
    Bulletin Polish Acad. Sci. Math. (rok: 2018, tom: 66, strony: 45-55), Wydawca: IMPAN
    Status:
    Published
    DOI:
    10.4064/ba8128-1-2018 - link to the publication
  42. Embedding Topological Dynamical Systems with Periodic Points in Cubical Shifts
    Authors:
    Yonatan Gutman
    Academic press:
    Ergodic Theory and Dynamical Systems (rok: 2017, tom: 37, strony: 512-538), Wydawca: Cambridge University Press
    Status:
    Published
    DOI:
    10.1017/etds.2015.40 - link to the publication
  43. Embedding minimal dynamical systems into Hilbert cubes
    Authors:
    Yonatan Gutman i Masaki Tsukamoto
    Academic press:
    Inventiones Math. (rok: 2020, tom: 221, strony: 113-166), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00222-019-00942-w - link to the publication
  44. Generic points for dynamical systems with average shadowing
    Authors:
    D. Kwietniak, M. Łącka, P. Oprocha
    Academic press:
    Monatshefte fur Mathematik (rok: 2017, tom: 183, strony: 625--648), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00605-016-1002-1 - link to the publication
  45. Higher order regionally proximal equivalence relations for general minimal group actions
    Authors:
    Yonatan Gutman, Eli Glasner and XiangDong Ye
    Academic press:
    Advances in Mathematics (rok: 2018, tom: 333, strony: 1004–1041), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2018.05.023 - link to the publication
  46. Lyapunov exponents and Oseledets decomposition in random dynamical systems generated by systems of delay differential equations
    Authors:
    Janusz Mierczyński, Sylvia Novo and Rafael Obaya
    Academic press:
    Communications on the Pure and Applied Analysis (rok: 2020, tom: 19, strony: 2235-2255), Wydawca: AIMS
    Status:
    Published
    DOI:
    10.3934/cpaa.2020098 - link to the publication
  47. Minimal models for actions of amenable groups
    Authors:
    Bartosz Frej and Dawid Huczek
    Academic press:
    Groups, Geometry and Dynamics (rok: 2017, tom: 11, strony: 567-583), Wydawca: EMS Publishing House
    Status:
    Published
    DOI:
    10.4171/GGD/408 - link to the publication
  48. On density of ergodic measures and generic points
    Authors:
    Katrin Gelfert i Dominik Kwietniak
    Academic press:
    Ergodic Theory and Dynamical Systems (rok: 2016, tom: online first, strony: 45314), Wydawca: Cambridge University Press
    Status:
    Published
    DOI:
    10.1017/etds.2016.97 - link to the publication
  49. On minimal homeomorphism and non-invertible maps preserving foliation
    Authors:
    Andrzej Biś i Wojciech Kozłowski
    Academic press:
    Topology and Its Application (rok: 2019, tom: 254, strony: 45302), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.topol.2018.11.024 - link to the publication
  50. Shearer's inequality and Infimum Rule for Shannon entropy and topological entropy
    Authors:
    Tomasz Downarowicz, Bartosz Frej and Pierre-Paul Romagnoli
    Academic press:
    Contemporary Mathematics (rok: 2016, tom: 669, strony: 63-75), Wydawca: American Mathematical Society
    Status:
    Published
    DOI:
    10.1090/conm/669 - link to the publication
  51. The structure theory of Nilspaces III: Inverse limit representations and topological dynamics
    Authors:
    Yonatan Gutman, Freddie Manners and Péter Varjú
    Academic press:
    Advances in Mathematics (rok: 2020, tom: 365, strony: 18994), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2020.107059 - link to the publication
  52. Topological and measure-theoretical entropies of nonautonomous dynamical systems
    Authors:
    Andrzej Biś
    Academic press:
    Journal of Dynamics and Differential Equations (rok: 2018, tom: 30, strony: 273-285), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10884-016-9554-2 - link to the publication
  53. Uniform generators, symbolic extensions with an embedding, and structure of periodic orbits
    Authors:
    David Burguet I Tomasz Downarowicz
    Academic press:
    Journal of Dynamics and Differential Equations (rok: 2018, tom: online, strony: 13881), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10884-018-9674-y - link to the publication
  54. Zero-dimensional isomorphic dynamical models
    Authors:
    Tomasz Downarowicz, Lei Jin, Wolfgang Lusky, and Yixiao Qiao
    Academic press:
    Ergodic Theory and Dynamical Systems (rok: 2018, tom: online, strony: 45306), Wydawca: Cambridge University Press
    Status:
    Published
    DOI:
    10.1017/etds.2018.131 - link to the publication
  55. Mean dimension and an embedding theorem for real flows
    Authors:
    Yonatan Gutman and Lei Jin
    Academic press:
    Fundamenta Mathematicae (rok: 2020, tom: 251, strony: 161-181), Wydawca: IMPAN
    Status:
    Accepted for publication
    DOI:
    10.4064/fm597-2-2020 - link to the publication
  56. Symbolic extensions of amenable group actions and the comparison property
    Authors:
    Tomasz Downarowicz and Guohua Zhang
    Academic press:
    Memoirs AMS , Wydawca: AMS
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication
  1. Topological and measure-theoretical entropies of solenoid
    Authors:
    A. Biś, A. Namiecińska
    Conference:
    Dynamical Systems Theory and Applications (rok: 2017, ), Wydawca: Springer
    Data:
    konferencja 11-14 grudnia 2017, Łódź
    Status:
    Published
  1. Topological and measure-theoretical entropies of a solenoid
    Authors:
    Andrzej Biś, Agnieszka Namiecińska
    Book:
    Dynamical systems in theoretical perspective (rok: 2018, tom: 248, strony: 37-50), Wydawca: Springer
    Status:
    Published
  2. Takens embedding theorem with a continuous observable
    Authors:
    Yonatan Gutman
    Book:
    Ergodic Theory: Advances in Dynamical Systems (rok: 2016, tom: bd, strony: 134-142), Wydawca: Walter de Gruyter GmbH & Co KG
    Status:
    Published

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