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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Lie systems and selected Lie theory methods in differential equations

2016/22/M/ST1/00542

Keywords:

Lie theory Lie systems discretization superposition rules supergeometry differential equations Schrödinger operators stochastic differential equationss

Descriptors:

  • ST1_10: Ordinary differential equations and dynamical systems
  • ST1_7: Lie groups, Lie algebras
  • ST1_5: Geometry

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 Polskiej Akademii Nauk

woj. mazowieckie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Janusz Grabowski 

Number of co-investigators in the project: 12

Call: HARMONIA 8 - announced on 2016-06-15

Amount awarded: 351 000 PLN

Project start date (Y-m-d): 2017-04-04

Project end date (Y-m-d): 2022-04-03

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.

Information in the final report

  • Publication in academic press/journals (21)
  • Articles in post-conference publications (4)
  1. Contact manifolds, Lagrangian Grassmannians and PDEs
    Authors:
    Olimjon Eshkobilov, Gianni Manno, Giovanni Moreno, and Katja Sagerschnig
    Academic press:
    Complex Manifolds (rok: 2018, tom: 5, strony: 26-88), Wydawca: De Gruyter
    Status:
    Published
    DOI:
    10.1515/coma-2018-0003 - link to the publication
  2. Geometric models for Lie-Hamilton systems on R^2
    Authors:
    J. Lange, J. de Lucas
    Academic press:
    Mathematics (rok: 2019, tom: 7, strony: 1053), Wydawca: MDPI
    Status:
    Published
    DOI:
    10.3390/math7111053 - link to the publication
  3. Multisymplectic structures and invariant tensors for Lie systems
    Authors:
    X. Grácia, J. de Lucas, M. Muñoz-Lecanda, S. Vilariño
    Academic press:
    J. Phys. A (rok: 2019, tom: 52, strony: 215201 (33pp)), Wydawca: IOP Science
    Status:
    Published
    DOI:
    10.1088/1751-8121/ab15f2 - link to the publication
  4. Odd connections on supermanifolds: existence and relation with affine connections
    Authors:
    Andrew James Bruce and Janusz Grabowski
    Academic press:
    J.Phys. A (rok: 2020, tom: 53, strony: 455203 (24pp)), Wydawca: IOPscience
    Status:
    Published
    DOI:
    10.1088/1751-8121/abb9f0 - link to the publication
  5. Poisson–Hopf deformations of Lie–Hamilton systems revisited: deformed superposition rules and applications to the oscillator algebra
    Authors:
    Angel Ballesteros, Rutwig Campoamor-Stursberg, Eduardo Fernández-Saiz, Francisco J Herranz and Javier de Lucas
    Academic press:
    Journal of Physics A: Mathematical and Theoretical (rok: 2021, tom: 54, strony: 205202), Wydawca: IOP Publishing
    Status:
    Published
    DOI:
    10.1088/1751-8121/abf1db - link to the publication
  6. SYMPLECTIC Z2n -MANIFOLDS
    Authors:
    Andrew James Bruce and Janusz Grabowski
    Academic press:
    JOURNAL OF GEOMETRIC MECHANICS (rok: 2021, tom: 13, strony: 285-311), Wydawca: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/jgm.2021020 - link to the publication
  7. VB-structures and generalizations
    Authors:
    Katarzyna Grabowska, Janusz Grabowski, Zohreh Ravanpak
    Academic press:
    Annals of Global Analysis and Geometry (rok: 2022, tom: published online, strony: 18264), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10455-022-09847-z - link to the publication
  8. A time-dependent energy-momentum method
    Authors:
    J.de Lucas, B.M.Zawora
    Academic press:
    Journal ofGeometryandPhysics (rok: 2021, tom: 170, strony: 104364), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.geomphys.2021.104364 - link to the publication
  9. Lie groupoids in information geometry
    Authors:
    K. Grabowska, J. Grabowski, M. Kuś, G. Marmo
    Academic press:
    J. Phys. A (rok: 2019, tom: 52, strony: 505202 (22pp)), Wydawca: IOP Science
    Status:
    Published
    DOI:
    10.1088/1751-8121/ab542e - link to the publication
  10. Lowest degree invariant second-order PDEs over rational homogeneous contact manifolds
    Authors:
    Dmitri V. Alekseevsky, Jan Gutt, Gianni Manno, Giovanni Moreno
    Academic press:
    Commun. Contemp. Math (rok: 2018, tom: 20, strony: 1750089 (54 pages)), Wydawca: World Scientific
    Status:
    Published
    DOI:
    10.1142/S0219199717500894 - link to the publication
  11. Nonassociative analogs of Lie groupoids
    Authors:
    JanuszGrabowski, ZohrehRavanpak
    Academic press:
    Differential Geometry and its Applications (rok: 2022, tom: 82, strony: 101887), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.difgeo.2022.101887 - link to the publication
  12. On the geometry of the Clairin theory of conditional symmetries for higher-order systems of PDEs with applications
    Authors:
    A.M. Grundland, J. de Lucas
    Academic press:
    Diff. Geom. Applications (rok: 2019, tom: 67, strony: 101557 (29 pages)), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.difgeo.2019.101557 - link to the publication
  13. Poisson-Hopf algebra deformations of Lie-Hamilton systems
    Authors:
    3.Angel Ballesteros1, Rutwig Campoamor-Stursberg, Eduardo Fernandez-Saiz, Francisco J. Herranz and Javier de Lucas
    Academic press:
    J. Phys. A (rok: 2018, tom: 51, strony: 065202 (25 pages)), Wydawca: IOP Science
    Status:
    Published
    DOI:
    10.1088/1751-8121/aaa090 - link to the publication
  14. Solvable Lie Algebras of Vector Fields and a Lie's Conjecture
    Authors:
    Katarzyna GRABOWSKA and Janusz GRABOWSKI
    Academic press:
    SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) (rok: 2020, tom: 16, strony: 065, 14 pages), Wydawca: National Academy of Sciences of Ukraine
    Status:
    Published
    DOI:
    10.3842/SIGMA.2020.065 - link to the publication
  15. Transitive Lie Algebras of Nilpotent Vector Fields and their Tanaka Prolongations
    Authors:
    Katarzyna Grabowska, Janusz Grabowski, Zohreh Ravanpak
    Academic press:
    Journal of Lie Theory (rok: 2021, tom: 31, strony: 1003-1014), Wydawca: Heldermann Verlag
    Status:
    Published
    DOI:
    brak - link to the publication
  16. A general method to construct invariant PDEs on homogeneous manifolds
    Authors:
    Dmitri V. Alekseevsky, Jan Gutt, Gianni Manno, Giovanni Moreno
    Academic press:
    Communications in Contemporary Mathematics (rok: 2022, tom: 24, strony: 2050089), Wydawca: World Scientific
    Status:
    Published
    DOI:
    10.1142/S0219199720500893 - link to the publication
  17. Darboux Families and the Classification of Real Four-Dimensional Indecomposable Coboundary Lie Bialgebras
    Authors:
    Javier de Lucas and Daniel Wysocki
    Academic press:
    Symmetry (rok: 2021, tom: 13, strony: 465), Wydawca: MDPI
    Status:
    Published
    DOI:
    10.3390/sym13030465 - link to the publication
  18. Discrete mechanics on unitary octonions
    Authors:
    Janusz Grabowski and Zohreh Ravanpak
    Academic press:
    International Journal of Geometric Methods in Modern Physics (rok: 2021, tom: 18, strony: 2150093), Wydawca: World Scientific
    Status:
    Published
    DOI:
    10.1142/S0219887821500936 - link to the publication
  19. Information Geometry on Groupoids: The Case of Singular Metrics
    Authors:
    Katarzyna Grabowska , Janusz Grabowski , Marek Kuś and Giuseppe Marmo
    Academic press:
    Open Systems & Information Dynamics (rok: 2020, tom: 27, strony: 2050015 (2020)), Wydawca: World Scientific
    Status:
    Published
    DOI:
    10.1142/S1230161220500158 - link to the publication
  20. Quasi-Lie schemes for PDEs
    Authors:
    J. F. Carinena, J. Grabowski, J. de Lucas
    Academic press:
    Int. J. Geom. Meth. Mod.Phys. (rok: 2019, tom: 19, strony: 1950096 (36 pages)), Wydawca: World Scientific
    Status:
    Published
    DOI:
    10.1142/S0219887819500968 - link to the publication
  21. Riemannian Structures on Zn2-Manifolds
    Authors:
    Andrew James Bruce and Janusz Grabowski
    Academic press:
    Mathematics (rok: 2020, tom: 8, strony: 1469), Wydawca: MDPI
    Status:
    Published
    DOI:
    10.3390/math8091469 - link to the publication
  1. An introduction to completely exceptional second order scalar partial differential equations
    Authors:
    Giovanni Moreno
    Conference:
    50th Seminar Sophus Lie" (rok: 2017, ), Wydawca: Banach Center Publications 113
    Data:
    konferencja 25.09.- 01.10, 2016
    Status:
    Published
  2. Complex contact manifolds, varieties of minimal rational tangents, and exterior differential systems
    Authors:
    J. Buczyński, G. Moreno
    Conference:
    Geometry of Lagrangian Grassmannians and nonlinear PDEs (rok: 2019, ), Wydawca: Banach Center Publications 117
    Data:
    konferencja September 5–9, 2016
    Status:
    Published
  3. Geometry of Lagrangian Grassmannians and nonlinear PDEs
    Authors:
    J. Gutt, G. Manno, G. Moreno
    Conference:
    Geometry of Lagrangian Grassmannians and nonlinear PDEs (rok: 2019, ), Wydawca: Banach Center Publications 117
    Data:
    konferencja September 5–9, 2016
    Status:
    Published
  4. A unified approach to Poisson–Hopf deformations of Lie–Hamilton systems based on sl(2)
    Authors:
    A. Ballesteros, R. Campoamor-Stursberg, E. Fernandez-Saiz, F.J. Heranz, J. de Lucas
    Conference:
    Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics (rok: 2018, ), Wydawca: Springer
    Data:
    konferencja 19-25 June, 2017
    Status:
    Published

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