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Geometric and analytic properties of ordinary differential equations

2017/25/B/ST1/00931

Keywords

Descriptors

  • ST1_10: Równania różniczkowe zwyczajne i układy dynamiczne

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

Voivodeship: 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
2018-01-19
Project end date
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. Laptopy Dell Vostro 3400 2 szt.
  2. Tablet IPad Pro 12,9".
  3. Urządzenie wielofunkcyjne HP M28W.
  4. notebook (2 pcs). Cost: 8 000 PLN
  5. skaner.

Information in the final report

Publication in academic press/journals (26)

  1. Normal forms, invariant manifolds and Lyapunov theorems

    Authors:
    Henryk Żołądek
    Academic press:
    Communications in Analysis and Mechanics (dawniej Journal of Geometric Mechanics) (year: 2023, volume: 15 (2), pages: 300 - 341), Publisher: AIMS
    Status:
    Published

  2. 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 (year: 2022, volume: 1,17152777777778, pages: 971-989), Publisher: Francis and Taylor
    Status:
    Published
    DOI:
    10.1080/10236198.2022.2103412 – link to the publication

  3. 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 (year: 2021, volume: 32, pages: 483--492), Publisher: Taylor & Francis Online
    Status:
    Published
    DOI:
    10.1080/10652469.2020.1809391 – link to the publication

  4. REGULARISING TRANSFORMATIONS FOR COMPLEX DIFFERENTIAL EQUATIONS WITH MOVABLE ALGEBRAIC SINGULARITIES

    Authors:
    Thomas Kecker, Galina Filipuk
    Academic press:
    Mathematical Physics, Analysis and Geometry (year: 2022, volume: 1,04791666666667, pages: 15707), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s11040-022-09417-6 – link to the publication

  5. 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 (year: 2021, volume: 22, pages: 133--141), Publisher: Miskolc University Press
    Status:
    Published
    DOI:
    10.18514/MMN.2021.2956 – link to the publication

  6. 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 (year: 2023, volume: 782, pages: 111-118), Publisher: American Mathematical Society
    Status:
    Published
    DOI:
    10.1090/conm/782/15724 – link to the publication

  7. 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 (year: 2022, volume: 148, pages: 17168), Publisher: Wiley
    Status:
    Published
    DOI:
    10.1111/sapm.12487 – link to the publication

  8. Regularising transformations for the (n, n + 1)-Liénard equations

    Authors:
    Galina Filipuk
    Academic press:
    Letters in Mathematical Physics (year: 2022, volume: 112, pages: 110), Publisher: Springer Nature
    Status:
    Published
    DOI:
    10.1007/s11005-022-01606-2 – link to the publication

  9. On singularities of certain non-linear second-order ordinary differential equations

    Authors:
    Galina Filipuk, Thomas Kecker
    Academic press:
    Results in Mathematics (year: 2021, volume: 77, pages: 41), Publisher: Birkhauser
    Status:
    Published
    DOI:
    10.1007/s00025-021-01577-1 – link to the publication

  10. 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 (year: 2018, volume: 7, pages: 1840005 (28 str.)), Publisher: World Scientic Publishing Company
    Status:
    Published
    DOI:
    10.1142/S2010326318400051 – link to the publication

  11. Perturbations of the Hess-Appelrot and Lagrange cases in the rigid body dynamics

    Authors:
    H. Żołądek
    Academic press:
    Journal of Geometry and Physics (year: 2019, volume: 142, pages: 121--136), Publisher: ELSEVIER
    Status:
    Published
    DOI:
    10.1016/j.geomphys.2019.04.001 – link to the publication

  12. On the derivatives of the Heun functions

    Authors:
    G. Filipuk, A. Ishkhanyanyz and Jan Dereziński
    Academic press:
    Journal of Contemporary Mathematical Analysis (year: 2020, volume: 55, pages: 21--29), Publisher: Armenian Academy of Sciences
    Status:
    Published

  13. 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 (year: 2019, volume: 11, pages: 47--65), Publisher: Univesidad de Jaen
    Status:
    Published

  14. A differential equation for varying Krall-type orthogonal polynomials

    Authors:
    G. Filipuk and J. F. Manas-Manas
    Academic press:
    Random Matrices: Theory and Applications (year: 2020, volume: 9, pages: 2040002 (15 pages)), Publisher: World Scientific Publishing Company
    Status:
    Published
    DOI:
    10.1142/S201032632040002X – link to the publication

  15. 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 (year: 2018, volume: 14, pages: 088 (19 pages)), Publisher: aa
    Status:
    Published
    DOI:
    10.3842/SIGMA.2018.088 – link to the publication

  16. Classification of Laguerre–Hahn orthogonal polynomials of class one

    Authors:
    G. Filipuk and M. N. Rebocho
    Academic press:
    Mathematische Nachrichten (year: 2019, volume: 293, pages: 244-262), Publisher: WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
    Status:
    Published
    DOI:
    10.1002/mana.201800063 – link to the publication

  17. 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 (year: 2020, volume: 1=43, pages: 2235 - 2253), Publisher: Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia
    Status:
    Published
    DOI:
    10.1007/s40840-019-00801-0 – link to the publication

  18. 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 (year: 2021, volume: 17, pages: 369-390), Publisher: Institute of Computer Science
    Status:
    Published
    DOI:
    10.20537/nd210402 – link to the publication

  19. Orthogonal polynomials, asymptotics and Heun functions

    Authors:
    Yang Chen, G. Filipuk, Longjun Zhan
    Academic press:
    Journal of Mathematical {Physics (year: 2019, volume: 60, pages: 113501, 35 pages), Publisher: AIP Publishing
    Status:
    Published
    DOI:
    10.1063/1.5102102 – link to the publication

  20. On the solutions of Okubo-type systems

    Authors:
    Galina Filipuk, Alberto Lastra
    Academic press:
    Hindawi Journal of Mathematics (year: 2021, volume: 2021, pages: Article ID 6690201, 5 pages), Publisher: Hindawi
    Status:
    Published
    DOI:
    10.1155/2021/6690201 – link to the publication

  21. 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 (year: 2020, volume: 9, pages: 2150029, 17 pages), Publisher: World Scientific Publishing Company
    Status:
    Published
    DOI:
    10.1142/S2010326321500295 – 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 (year: 2020, volume: 53, pages: 495201, 29 pages), Publisher: IOP Science
    Status:
    Published
    DOI:
    10.1088/1751-8121/abbd54 – link to the publication

  23. Analytic properties of the complete normal form for the Bogdanov--Takens singularity

    Authors:
    Ewa Stróżyna, Henryk Żołądek
    Academic press:
    Nonlinearity (year: 2021, volume: 34, pages: 3046--3062), Publisher: IOP Publishing
    Status:
    Published
    DOI:
    10.1088/1361-6544/abe51d – link to the publication

  24. 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 (year: 2018, volume: 334, pages: 356 - 366), Publisher: ELSEVIER
    Status:
    Published
    DOI:
    10.1016/j.amc.2018.04.022 – link to the publication

  25. 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 (year: 2018, volume: 41, pages: 2442 - 2465), Publisher: WILEY
    Status:
    Published
    DOI:
    10.1002/mma.4751 – link to the publication

  26. 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
    Status:
    Accepted for publication

Book publications / chapters in book publications (6)

  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 (year: 2023, volume: 1, pages: 268), Publisher: World Scientific Publishing Europe Ltd.
    Status:
    Published

  2. 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 (year: 2020, volume: 1425, pages: 12107), Publisher: IOP Publishing
    Status:
    Published

  3. Melnikov functions in the rigid body dynamics

    Authors:
    P. Lubowiecki and H. Żołądek
    Book:
    Geometric Methods in Physics XXXVII Workshop 2018 (year: 2019, volume: 1, pages: 75-82), Publisher: Birkhauser
    Status:
    Published

  4. 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 (year: 2018, volume: 256, pages: 251--161), Publisher: Springer Nature
    Status:
    Published

  5. 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 (year: 2021, volume: 1, pages: 99--106), Publisher: De Gruyter Poland Sciendo
    Status:
    Published

  6. A note on the commutator of hamiltonian vector fields

    Authors:
    H. Żołądek
    Book:
    Volume dedicated to Emma Previato (year: 2020, volume: 1, pages: 57--63), Publisher: SPRINGER
    Status:
    Published

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