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Application of differential Galois theory to integrability studies of nonlinear dynamical systems

2013/09/B/ST1/04130

Keywords

Descriptors

  • ST1_12: Fizyka matematyczna
  • ST1_10: Równania różniczkowe zwyczajne i układy dynamiczne
  • ST1_4: Geometria algebraiczna i zespolona

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

Voivodeship: lubuskie

Other projects carried out by the institution »

Principal investigator (from the host institution)

dr hab. Maria Przybylska

Number of co-investigators in the project: 5

Call

OPUS 5 – announced on 2013-03-15

Amount awarded
347 370 PLN
Project start date
2014-02-20
Project end date
2017-10-19
Project duration
44 months (the same as in the proposal)
Project status
Project settled

Equipment purchased [PL]

  1. jednoroczny kontrakt do zakupionej wcześniej licencji programu Mathematica. Cost: 1 300 PLN
  2. licencja programu Maple z trzyletnim kontraktem. Cost: 7 000 PLN
  3. notebook (2 pcs). Cost: 14 000 PLN
  4. nowa licencja programu Mathematica z trzyletnim kontraktem. Cost: 8 000 PLN

Information in the final report

Publication in academic press/journals (14)

  1. Global Properties of Kovalevskaya Exponents

    Authors:
    Andrzej J. Maciejewski, Maria Przybylska
    Academic press:
    Regular and Chaotic Dynamics (year: 2017, volume: 22, pages: 840–850), Publisher: Springer
    Status:
    Published
    DOI:
    10.1134/S1560354717070061 – link to the publication

  2. The inhomogeneous Suslov problem

    Authors:
    Luis C. Garcia-Naranjo, Andrzej J. Maciejewski, Juan C. Marrero, Maria Przybylska
    Academic press:
    Physics Letters A (year: 2014, volume: 378, pages: 2389--2394), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.physleta.2014.06.026 – link to the publication

  3. Note on integrability of certain homogeneous Hamiltonian systems

    Authors:
    Wojciech Szumiński, Andrzej J. Maciejewski, Maria Przybylska
    Academic press:
    Physics Letters A (year: 2015, volume: 379, pages: 2970-2976), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.physleta.2015.08.032 – link to the publication

  4. Dynamics of multibody chains in circular orbit: non-integrability of equations of motion

    Authors:
    Andrzej J. Maciejewski, Maria Przybylska
    Academic press:
    Celestial Mechanics and Dynamical Astronomy (year: 2016, volume: 126, pages: 297-311), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s10569-016-9696-x – link to the publication

  5. Anisotropic Kepler and anisotropic two fixed centres problems

    Authors:
    Andrzej J. Maciejewski, Maria Przybylska, Wojciech Szumiński
    Academic press:
    Celestial Mechanics and Dynamical Astronomy (year: 2017, volume: 127, pages: 163-184), Publisher: Sringer
    Status:
    Published
    DOI:
    10.1007/s10569-016-9722-z – link to the publication

  6. Note on integrability of certain homogeneous Hamiltonian systems in 2D constant curvature spaces

    Authors:
    Andrzej J. Maciejewski, Wojciech Szumiński, Maria Przybylska
    Academic press:
    Physics Letters A (year: 2017, volume: 381, pages: 725-732), Publisher: Elsvier
    Status:
    Published
    DOI:
    10.1016/j.physleta.2016.12.030 – link to the publication

  7. Integrability of Hamiltonian systems with algebraic potentials

    Authors:
    Andrzej J. Maciejewski, Maria Przybylska
    Academic press:
    Physics Letters A (year: 2016, volume: 380, pages: 76-82), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.physleta.2015.08.035 – link to the publication

  8. Understanding reversals of a rattleback

    Authors:
    Stefan Rauch-Wojciechowski, Maria Przybylska
    Academic press:
    Regular and Chaotic Dynamics (year: 2017, volume: 22, pages: 368-385), Publisher: Springer
    Status:
    Published
    DOI:
    10.1134/S1560354717040037 – link to the publication

  9. Dynamics of a rolling and sliding disk in a plane. Asymptotic solutions, stability and numerical simulations

    Authors:
    Maria Przybylska, Stefan Rauch-Wojciechowski
    Academic press:
    Regular and Chaotic Dynamics (year: 2016, volume: 21, pages: 204-231), Publisher: Springer
    Status:
    Published
    DOI:
    10.1134/S1560354716020052 – link to the publication

  10. Integrability analysis of chaotic and hyperchaotic finance systems

    Authors:
    Wojciech Szumiński
    Academic press:
    Nonlinear Dynamics (year: 2018, volume: 94, pages: 443-459), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s11071-018-4370-3 – link to the publication

  11. Dynamics of constrained many body problems in constant curvature two-dimensional manifolds

    Authors:
    Andrzej J. Maciejewski, Maria Przybylska
    Academic press:
    Philosophical Transactions of the Royal Society A (year: 2018, volume: 376, pages: 20170425-1-18), Publisher: The Royal Society.
    Status:
    Published
    DOI:
    10.1098/rsta.2017.0425 – link to the publication

  12. The Euler-Poisson Equations; an elementary approach to integrability conditions

    Authors:
    Sasho Popov, Jean-Marie Strelcyn
    Academic press:
    Journal of Geometric Mechanics (year: 2018, volume: 10, pages: 293-329), Publisher: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/jgm.2018011 – link to the publication

  13. Non-integrability of restricted double pendula

    Authors:
    Tomasz Stachowiak, Wojciech Szumiński
    Academic press:
    Physics Letters A (year: 2015, volume: 379, pages: 3017–3024), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.physleta.2015.09.052 – link to the publication

  14. Hypergeometric first integrals of the Duffing and van der Pol oscillators

    Authors:
    Tomasz Stachowiak
    Academic press:
    Journal of Differential Equations (year: 2019, volume: 266, pages: 5895–5911), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2018.10.049 – link to the publication

Book publications / chapters in book publications (1)

  1. Analysis of the constrained 2-body problem

    Authors:
    Wojciech Szumiński, Tomasz Stachowiak
    Book:
    Dynamical Systems: Theoretical and Experimental Analysis. (year: 2016, volume: 182, pages: 361-372), Publisher: Springer Proceedings in Mathematics & Statistics
    Status:
    Published
    DOI:
    link to the publication

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