Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

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Integrability, non-integrability and chaos in multi-dimensional dynamical systems

2020/39/D/ST1/01632

Keywords:

Dynamical systems integrability non-integrability chaos differential Galois theory Hamiltonian systems in curved spaces non-Hamiltonian systems.

Descriptors:

  • ST1_010:
  • ST1_012:

Panel:

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

Host institution :

Uniwersytet Zielonogórski, Wydział Fizyki i Astronomii

woj. lubuskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

dr Wojciech Szumiński 

Number of co-investigators in the project: 3

Call: SONATA 16 - announced on 2020-09-15

Amount awarded: 298 080 PLN

Project start date (Y-m-d): 2021-06-24

Project end date (Y-m-d): 2026-06-23

Project duration:: 60 months (the same as in the proposal)

Project status: Project completed

Project description

Download the project description in a pdf file

Note - project descriptions were prepared by the authors of the applications themselves and placed in the system in an unchanged form.

Information in the final report

  • Publication in academic press/journals (19)
  1. Translational dynamics of diatomic molecule in magnetic quadrupole trap
    Authors:
    Yurij Yaremko, Maria Przybylska, Andrzej Maciejewski
    Academic press:
    The Journal of Chemical Physics (rok: 2025, tom: 163, strony: 154305), Wydawca: AIP Publishing
    Status:
    Published
    DOI:
    10.1063/5.0291088 - link to the publication
  2. Integrability of the generalised Hill problem
    Authors:
    Thierry Combot, Andrzej J. Maciejewski, Maria Przybylska
    Academic press:
    Nonlinear Dynamics (rok: 2021, tom: 107, strony: 1989–2002), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11071-021-07040-8 - link to the publication
  3. Dynamics and integrability of the swinging Atwood machine generalisations
    Authors:
    Wojciech Szumiński, Andrzej, J. Maciejewski
    Academic press:
    Nonlinear Dynamics (rok: 2022, tom: 110, strony: 2101–2128), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11071-022-07680-4 - link to the publication
  4. Top on a smooth plane
    Authors:
    Maria Przybylska, Andrzej J. Maciejewski
    Academic press:
    Chaos: An Interdisciplinary Journal of Nonlinear Science (rok: 2024, tom: 34, strony: 46046), Wydawca: AIP Publishing
    Status:
    Published
    DOI:
    10.1063/5.0200592 - link to the publication
  5. Diatomic molecule in the polar trap
    Authors:
    Yurij Yaremko, Maria Przybylska, Andrzej J Maciejewski
    Academic press:
    Journal of Physics B: Atomic, Molecular and Optical Physics (rok: 2025, tom: 58, strony: 55101), Wydawca: IOP Publishing
    Status:
    Published
    DOI:
    10.1088/1361-6455/adb46b - link to the publication
  6. Dynamics and non-integrability of the variable-length double pendulum: exploring chaos and periodicity via the Lyapunov refined maps
    Authors:
    Wojciech Szumiński, Tomasz Kapitaniak
    Academic press:
    Journal of Sound and Vibration (rok: 2025, tom: 611, strony: 119099), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jsv.2025.119099 - link to the publication
  7. Chaos and integrability of relativistic homogeneous potentials in curved space
    Authors:
    Wojciech Szumiński, Maria Przybylska, Andrzej, J. Maciejewski
    Academic press:
    Nonlinear Dynamics (rok: 2024, tom: 112, strony: 4879–4898), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11071-023-09224-w - link to the publication
  8. Destructive relativity
    Authors:
    Maria Przybylska, Wojciech Szumiński, Andrzej J. Maciejewski
    Academic press:
    Chaos (rok: 2023, tom: 33, strony: 63156), Wydawca: AIP Publishing
    Status:
    Published
    DOI:
    10.1063/5.0140633 - link to the publication
  9. Integrability of Hamiltonian systems with gyroscopic term
    Authors:
    Maria Przybylska, Andrzej J. Maciejewski
    Academic press:
    Nonlinear Dynamics (rok: 2022, tom: 11, strony: 275–287), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11071-022-07866-w - link to the publication
  10. Non-integrability of charged three-body problem
    Authors:
    Maria Przybylska, Andrzej J. Maciejewski
    Academic press:
    Celestial Mechanics and Dynamical Astronomy (rok: 2025, tom: 137, strony: 46030), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10569-025-10237-3 - link to the publication
  11. Integrability of certain Hamiltonian systems in 2D variable curvature spaces
    Authors:
    Wojciech Szumiński, Adel A. Elmandouh
    Academic press:
    Europhysics Letters (rok: 2025, tom: 150, strony: 12002), Wydawca: IOPscience
    Status:
    Published
    DOI:
    10.1209/0295-5075/adc150 - link to the publication
  12. A new model of variable-length coupled pendulums: from hyperchaos to superintegrability
    Authors:
    Wojciech Szumiński
    Academic press:
    Nonlinear Dynamics (rok: 2024, tom: 112, strony: 4117–4145), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11071-023-09253-5 - link to the publication
  13. When Knowledge of a Single Integral of Motion is Sufficient for Integration of Newton Equations $ddot q= M(q)$
    Authors:
    Stefan Rauch-Wojciechowski, Maria Przybylska
    Academic press:
    Regular and Chaotic Dynamics (rok: 2025, tom: 30, strony: 866–885), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1134/S1560354725050077 - link to the publication
  14. Non-Integrability of the Kepler and the Two-Body Problems on the Heisenberg Group
    Authors:
    Tomasz Stachowiak, Andrzej J. Maciejewski
    Academic press:
    Symmetry, Integrability and Geometry: Methods and Applications (rok: 2021, tom: 17, strony: 46024), Wydawca: SIGMA
    Status:
    Published
    DOI:
    10.3842/SIGMA.2021.074 - link to the publication
  15. The geodesic flow of the BGPP metric is Liouville integrable
    Authors:
    Andrzej J Maciejewski, Maria Przybylska, Galliano Valent
    Academic press:
    Classical and Quantum Gravity (rok: 2023, tom: 40, strony: 155007), Wydawca: IOPscience
    Status:
    Published
    DOI:
    10.1088/1361-6382/ace097 - link to the publication
  16. Non-integrability of the planar elliptic restricted three-body problem
    Authors:
    Maria Przybylska, Andrzej J. Maciejewski
    Academic press:
    Celestial Mechanics and Dynamical Astronomy (rok: 2023, tom: 135, strony: 46044), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10569-022-10120-5 - link to the publication
  17. Dynamics and non-integrability of the double spring pendulum
    Authors:
    Wojciech Szumiński, Andrzej J. Maciejewski
    Academic press:
    Journal of Sound and Vibration (rok: 2024, tom: 589, strony: 118550), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jsv.2024.118550 - link to the publication
  18. Non-integrability of a model of elastic dumbbell satellite
    Authors:
    Thierry Combot, Andrzej J. Maciejewski, Maria Przybylska
    Academic press:
    Nonlinear Dynamics (rok: 2021, tom: 106, strony: 125–146), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11071-021-06771-y - link to the publication
  19. Integrability and chaos of relativistic Hamiltonian systems in 2D Riemannian manifolds
    Authors:
    Wojciech Szumiński, Maria Przybylska
    Academic press:
    Nonlinear Dynamics (rok: 2025, tom: 113, strony: 30057–30085), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11071-025-11554-w - link to the publication

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