Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

Equipment

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Geometric and analytic properties of ordinary differential equations

2017/25/B/ST1/00931

Keywords:

holomorphic foliations limit cycles normal forms of vector fields hypergeometric equations multiply orthogonal polynomials mechanical systems

Descriptors:

  • ST1_10: Ordinary differential equations and dynamical systems

Panel:

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

Host institution :

Uniwersytet Warszawski, Wydział Matematyki, Informatyki i Mechaniki

woj. mazowieckie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Henryk Żołądek 

Number of co-investigators in the project: 4

Call: OPUS 13 - announced on 2017-03-15

Amount awarded: 288 000 PLN

Project start date (Y-m-d): 2018-01-19

Project end date (Y-m-d): 2023-01-18

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

Project status: Project settled

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.

Equipment purchased [PL]

  1. Urządzenie wielofunkcyjne HP M28W.
  2. notebook (2 szt.) (8 000 PLN)
  3. skaner.
  4. Tablet IPad Pro 12,9".
  5. Laptopy Dell Vostro 3400 2 szt.

Information in the final report

  • Publication in academic press/journals (29)
  • Book publications / chapters in book publications (6)
  1. Classification of Laguerre–Hahn orthogonal polynomials of class one
    Authors:
    G. Filipuk and M. N. Rebocho
    Academic press:
    Mathematische Nachrichten (rok: 2019, tom: 293, strony: 244-262), Wydawca: WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
    Status:
    Published
    DOI:
    10.1002/mana.201800063 - link to the publication
  2. Normal forms, invariant manifolds and Lyapunov theorems
    Authors:
    Henryk Żołądek
    Academic press:
    Communications in Analysis and Mechanics (dawniej Journal of Geometric Mechanics) (rok: 2023, tom: 15 (2), strony: 300 - 341), Wydawca: AIMS
    Status:
    Published
    DOI:
    brak - link to the publication
  3. On the derivatives of the Heun functions
    Authors:
    G. Filipuk, A. Ishkhanyanyz and Jan Dereziński
    Academic press:
    Journal of Contemporary Mathematical Analysis (rok: 2020, tom: 55, strony: 21--29), Wydawca: Armenian Academy of Sciences
    Status:
    Published
    DOI:
    brak - link to the publication
  4. QUALITATIVE ANALYSIS OF SOME LIBRATION POINTS IN THE RESTRICTED FOUR BODY PROBLEM
    Authors:
    A. Ligęza and H. Żołądek
    Academic press:
    Russian Journal of Nonlinear Dynamics (rok: 2021, tom: 17, strony: 369-390), Wydawca: Institute of Computer Science
    Status:
    Published
    DOI:
    10.20537/nd210402 - link to the publication
  5. Second–order difference equation for Sobolev–type orthogonal polynomials. Part II: computational tools
    Authors:
    Galina Filipuk, Juan F. Mañas–Mañas and Juan J. Moreno–Balcázar
    Academic press:
    East Asian Journal on Applied Mathematics (rok: 2023, ), Wydawca: Global-Science Press
    Status:
    Accepted for publication
    DOI:
    10.4208/eajam.2022-235.190223 - link to the publication
  6. Remarks about moduli
    Authors:
    H. Żołądek
    Academic press:
    Journal of the Belarussian State University. Mathematics and Informatics , Wydawca: Belarussian State University
    Status:
    Submitted
    DOI:
    brak - link to the publication
  7. Analytic properties of the complete normal form for the Bogdanov--Takens singularity
    Authors:
    Ewa Stróżyna, Henryk Żołądek
    Academic press:
    Nonlinearity (rok: 2021, tom: 34, strony: 3046--3062), Wydawca: IOP Publishing
    Status:
    Published
    DOI:
    10.1088/1361-6544/abe51d - link to the publication
  8. Differential and difference equations for recurrence coefficients of orthogonal polynomials with hypergeometric weights and Backlund transformations of the sixth Painleve equation
    Authors:
    Jie Hu, G. Filipuk, Yang Chen
    Academic press:
    Random Matrices: Theory and Applications (rok: 2020, tom: 9, strony: 2150029, 17 pages), Wydawca: World Scientific Publishing Company
    Status:
    Published
    DOI:
    10.1142/S2010326321500295 - link to the publication
  9. Ladder operators and a differential equation for varying generalized Freud-type orthogonal polynomials
    Authors:
    G. Filipuk, J. F. Manas-Manas, J. J. Moreno-Balcazar
    Academic press:
    Random Matrices: Theory and Applications (rok: 2018, tom: 7, strony: 1840005 (28 str.)), Wydawca: World Scientic Publishing Company
    Status:
    Published
    DOI:
    10.1142/S2010326318400051 - link to the publication
  10. Nonlinear difference equations for a modified Laguerre weight: Laguerre-Freud equations and asymptotics
    Authors:
    Y. Chen, G. Filipuk and M. N. Rebocho
    Academic press:
    Jaen Journal of Mathematics (rok: 2019, tom: 11, strony: 47--65), Wydawca: Univesidad de Jaen
    Status:
    Published
    DOI:
    brak - link to the publication
  11. REGULARISING TRANSFORMATIONS FOR COMPLEX DIFFERENTIAL EQUATIONS WITH MOVABLE ALGEBRAIC SINGULARITIES
    Authors:
    Thomas Kecker, Galina Filipuk
    Academic press:
    Mathematical Physics, Analysis and Geometry (rok: 2022, tom: 1,04791666666667, strony: 15707), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11040-022-09417-6 - link to the publication
  12. The Symmetric Semi-classical Orthogonal Polynomials of Class Two and Some of Their Extensions
    Authors:
    G. Filipuk and Rebocho
    Academic press:
    Bulletin of the Malaysyan Mathematical Sciences Society (rok: 2020, tom: 1=43, strony: 2235 - 2253), Wydawca: Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia
    Status:
    Published
    DOI:
    10.1007/s40840-019-00801-0 - link to the publication
  13. A differential equation for varying Krall-type orthogonal polynomials
    Authors:
    G. Filipuk and J. F. Manas-Manas
    Academic press:
    Random Matrices: Theory and Applications (rok: 2020, tom: 9, strony: 2040002 (15 pages)), Wydawca: World Scientific Publishing Company
    Status:
    Published
    DOI:
    10.1142/S201032632040002X - link to the publication
  14. Orthogonal polynomials, asymptotics and Heun functions
    Authors:
    Yang Chen, G. Filipuk, Longjun Zhan
    Academic press:
    Journal of Mathematical {Physics (rok: 2019, tom: 60, strony: 113501, 35 pages), Wydawca: AIP Publishing
    Status:
    Published
    DOI:
    10.1063/1.5102102 - link to the publication
  15. Perturbations of the Hess-Appelrot and Lagrange cases in the rigid body dynamics
    Authors:
    H. Żołądek
    Academic press:
    Journal of Geometry and Physics (rok: 2019, tom: 142, strony: 121--136), Wydawca: ELSEVIER
    Status:
    Published
    DOI:
    10.1016/j.geomphys.2019.04.001 - link to the publication
  16. PSEUDO-ABELIAN INTEGRALS AND DIVERGENCE INTEGRALS ON SLOW-FAST MODEL SYSTEM
    Authors:
    Maqrcin Bobieński and Michał Nagrodzki
    Academic press:
    Buletin des Sciences Mathematiques , Wydawca: Elsevier
    Status:
    Submitted
    DOI:
    Brak - link to the publication
  17. A characterization theorem for semi-classical orthogonal polynomials on non-uniform lattices
    Authors:
    A. Branquinho , Y. Chen G. Filipuk, M. N. Rebocho
    Academic press:
    Applied Mathematics and Computation (rok: 2018, tom: 334, strony: 356 - 366), Wydawca: ELSEVIER
    Status:
    Published
    DOI:
    10.1016/j.amc.2018.04.022 - link to the publication
  18. Differential equations for the recurrence coefficients of semiclassical orthogonal polynomials and their relation to the Painlevé equations via the geometric approach
    Authors:
    Anton Dzhamay, Galina Filipuk and Alexander Stokes
    Academic press:
    Studies in Applied Mathematics (rok: 2022, tom: 148, strony: 17168), Wydawca: Wiley
    Status:
    Published
    DOI:
    10.1111/sapm.12487 - link to the publication
  19. Discrete Orthogonal Polynomials with Hypergeometric Weights and Painleve VI
    Authors:
    G. Filipuk and W. van Asche
    Academic press:
    Symmetry, Integrability and Geometry: Methods and Applications SIGMA (rok: 2018, tom: 14, strony: 088 (19 pages)), Wydawca: aa
    Status:
    Published
    DOI:
    10.3842/SIGMA.2018.088 - link to the publication
  20. Linear equations with one constraint and their connection to nonlinear equations of the fourth order
    Authors:
    Alexander Chichurin, Galina Filipuk
    Academic press:
    Miskolc Mathematical Notes (rok: 2021, tom: 22, strony: 133--141), Wydawca: Miskolc University Press
    Status:
    Published
    DOI:
    10.18514/MMN.2021.2956 - link to the publication
  21. On differential systems related to generalized Meixner and deformed Laguerre orthogonal polynomials
    Authors:
    Anton Dzhamay, Galina Filipuk, Alexander Stokes
    Academic press:
    Integral Transforms and Special Functions (rok: 2021, tom: 32, strony: 483--492), Wydawca: Taylor & Francis Online
    Status:
    Published
    DOI:
    10.1080/10652469.2020.1809391 - link to the publication
  22. Recurrence coefficients for discrete orthogonal polynomials with hypergeometric weight and discrete Painleve equations
    Authors:
    Anton Dzhamay, G. Filipuk, Alexandet Stokes
    Academic press:
    Journal of Physics A: Mathematical and Theoretical (rok: 2020, tom: 53, strony: 495201, 29 pages), Wydawca: IOP Science
    Status:
    Published
    DOI:
    10.1088/1751-8121/abbd54 - link to the publication
  23. Regularising transformations for the (n, n + 1)-Liénard equations
    Authors:
    Galina Filipuk
    Academic press:
    Letters in Mathematical Physics (rok: 2022, tom: 112, strony: 110), Wydawca: Springer Nature
    Status:
    Published
    DOI:
    10.1007/s11005-022-01606-2 - link to the publication
  24. Invariants of group representations, dimension/degree duality and normal forms of vector fields
    Authors:
    E. Stróżyna and H. Żołądek
    Academic press:
    Bulletin des Sciences Mathematiques , Wydawca: ELSEVIER
    Status:
    Submitted
    DOI:
    brak - link to the publication
  25. A system of nonlinear difference equations for recurrence relation coefficients of a modified Jacobi weight
    Authors:
    Yang Chen, Galina Filipuk, and Maria das Neves Rebocho
    Academic press:
    Contemporary Mathematics (rok: 2023, tom: 782, strony: 111-118), Wydawca: American Mathematical Society
    Status:
    Published
    DOI:
    10.1090/conm/782/15724 - link to the publication
  26. Nonlinear difference equations arising from the generalized Stieltjes-Wigert and q-Laguerre weights
    Authors:
    H. Chen, G. Filipuk, Y. Chen
    Academic press:
    Mathematical Methods in Applied Sciences (rok: 2018, tom: 41, strony: 2442 - 2465), Wydawca: WILEY
    Status:
    Published
    DOI:
    10.1002/mma.4751 - link to the publication
  27. On singularities of certain non-linear second-order ordinary differential equations
    Authors:
    Galina Filipuk, Thomas Kecker
    Academic press:
    Results in Mathematics (rok: 2021, tom: 77, strony: 41), Wydawca: Birkhauser
    Status:
    Published
    DOI:
    10.1007/s00025-021-01577-1 - link to the publication
  28. On the solutions of Okubo-type systems
    Authors:
    Galina Filipuk, Alberto Lastra
    Academic press:
    Hindawi Journal of Mathematics (rok: 2021, tom: 2021, strony: Article ID 6690201, 5 pages), Wydawca: Hindawi
    Status:
    Published
    DOI:
    10.1155/2021/6690201 - link to the publication
  29. Second-order difference equation for Sobolev-type orthogonal polynomials: Part I: theoretical results
    Authors:
    Galina Filipuk, Juan F. Mañas-Mañas and Juan J. Moreno-Balcázar
    Academic press:
    Journal of Difference Equations and Applications (rok: 2022, tom: 1,17152777777778, strony: 971-989), Wydawca: Francis and Taylor
    Status:
    Published
    DOI:
    10.1080/10236198.2022.2103412 - link to the publication
  1. Qualitative Theory of ODEs. An Introduction to Dynamical Systems Theory
    Authors:
    Henryk Żołądek and Raul Murillo
    Book:
    Qualitative Theory of ODEs. An Introduction to Dynamica Systems Theory (rok: 2023, tom: 1, strony: 268), Wydawca: World Scientific Publishing Europe Ltd.
    Status:
    Published
  2. A note on the commutator of hamiltonian vector fields
    Authors:
    H. Żołądek
    Book:
    Volume dedicated to Emma Previato (rok: 2020, tom: 1, strony: 57--63), Wydawca: SPRINGER
    Status:
    Published
  3. Melnikov functions in the rigid body dynamics
    Authors:
    P. Lubowiecki and H. Żołądek
    Book:
    Geometric Methods in Physics XXXVII Workshop 2018 (rok: 2019, tom: 1, strony: 75-82), Wydawca: Birkhauser
    Status:
    Published
  4. On a regularisation of a nonlinear differential equation related to the non-homogeneous Airy equation
    Authors:
    Galina Filipuk, Thomas Kecker, Frederico Zulo
    Book:
    Proceedings of the Contemporary Mathematics in Kielce 2020 (rok: 2021, tom: 1, strony: 99--106), Wydawca: De Gruyter Poland Sciendo
    Status:
    Published
  5. Symmetric semi-classical orthogonal polynomials of class one on q-quadratic lattices
    Authors:
    G. Filipuk, M. N. Rebocho
    Book:
    Formal and Analytic Solutions of Differential Equations (rok: 2018, tom: 256, strony: 251--161), Wydawca: Springer Nature
    Status:
    Published
  6. The properties of certain linear and nonlinear differential equations of the fourth order arising in beam models
    Authors:
    Chichurin and G. Filipuk
    Book:
    IOP Conf. Series: Journal of Physics: Conf. Series. Modelling and Methods of Structural Analysis (rok: 2020, tom: 1425, strony: 12107), Wydawca: IOP Publishing
    Status:
    Published

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