Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

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Geometric methods and rigorous numerics in the n-body problem

2019/35/B/ST1/00655

Keywords:

dynamical systems n-body problem rigorous numerics invariant manifolds central configurations regularisation

Descriptors:

  • ST1_010:
  • ST1_012:
  • ST1_017:

Panel:

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

Host institution :

Uniwersytet Jagielloński, Wydział Matematyki i Informatyki

woj. małopolskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Piotr Zgliczyński 

Number of co-investigators in the project: 3

Call: OPUS 18 - announced on 2019-09-16

Amount awarded: 360 132 PLN

Project start date (Y-m-d): 2020-06-25

Project end date (Y-m-d): 2024-09-24

Project duration:: 51 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 (14)
  1. Computer Assisted Proof of Drift Orbits Along Normally Hyperbolic Manifolds II: Application to the Restricted Three Body Problem
    Authors:
    M. J. Capiński, N. Wodka
    Academic press:
    Commun. Nonlinear Sci. Numer. Simul. (rok: 2022, tom: 111, strony: 45685), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2022.106424 - link to the publication
  2. The number of relative equilibria in the PCR4BP
    Authors:
    J.L. Figueras, W. Tucker, P. Zgliczyński
    Academic press:
    Journal of Dynamics and Differential Equations (rok: 2022, tom: 1, strony: 18629), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10884-022-10230-6 - link to the publication
  3. Computer assisted proofs for transverse collision and near collision orbits in the restricted three body problem
    Authors:
    M. J. Capiński, S. Kepley, J. D. Mireles James
    Academic press:
    Journal of Differential Equations (rok: 2023, tom: 366, strony: 132-191), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2023.03.053 - link to the publication
  4. Central configurations on the plane with N heavy and k light bodies
    Authors:
    Małgorzata Moczurad, Piotr Zgliczyński
    Academic press:
    Commun. Nonlinear Sci. Numer. Simul. (rok: 2022, tom: 114, strony: 45688), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2022.106533 - link to the publication
  5. Oscillatory Motions and Parabolic Manifolds at Infinity in the Planar Circular Restricted Three Body Problem
    Authors:
    Capiński, Guardia, Martin, Seara, Zgliczyński
    Academic press:
    Journal of Differential Equations (rok: 2022, tom: 320, strony: 316--370), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2022.02.056 - link to the publication
  6. Central configurations on the plane with N heavy and k light bodies
    Authors:
    Małgorzata Moczurad, Piotr Zgliczyński
    Academic press:
    Commun. Nonlinear Sci. Numer. Simul. (rok: 2022, tom: 114, strony: 45688), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2022.106533 - link to the publication
  7. Breakdown of homoclinic orbits to L3: Nonvanishing of the Stokes constant
    Authors:
    Inmaculada Baldomá, Maciej J. Capiński, Mar Giralt, Marcel Guardia
    Academic press:
    Discrete and Continuous Dynamical Systems (rok: 2025, tom: 45, 1, strony: 56-88), Wydawca: American Institute of Mathematical Sciences (AIMS)
    Status:
    Published
    DOI:
    10.3934/dcds.2024086 - link to the publication
  8. Recent advances in rigorous computation of Poincare maps
    Authors:
    Tomasz Kapela, Daniel Wilczak, P. Zgliczynski
    Academic press:
    Commun. Nonlinear Sci. Numer. Simul. (rok: 2022, tom: 110, strony: 45679), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2022.106366 - link to the publication
  9. The number of relative equilibria in the PCR4BP
    Authors:
    J.L. Figueras, W. Tucker, P. Zgliczyński
    Academic press:
    Journal of Dynamics and Differential Equations (rok: 2022, tom: 1, strony: 18629), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10884-022-10230-6 - link to the publication
  10. Central configurations in spatial $n$-body problem for n=5,6 with equal masses
    Authors:
    Małgorzata Moczurad, Piotr Zgliczyński
    Academic press:
    Celestial Mechanics and Dynamical Astronomy (rok: 2020, tom: 132, strony: 56), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10569-020-09993-1 - link to the publication
  11. Breakdown of Heteroclinic Connections in the Analytic Hopf-Zero Singularity: Rigorous Computation of the Stokes Constant
    Authors:
    I. Baldomá, M. J. Capiński, M. Guardia, T. M. Seara
    Academic press:
    Journal of Nonlinear Science (rok: 2023, tom: 33, strony: 17168), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00332-022-09882-x - link to the publication
  12. Characterising blenders via covering relations and cone conditions
    Authors:
    Maciej J. Capiński, Bernd Krauskopf, Hinke M. Osinga, Piotr Zgliczyński
    Academic press:
    Journal of Differential Equations (rok: 2025, tom: 416, strony: 768--805), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.004 - link to the publication
  13. Computer Assisted Proof of Drift Orbits Along Normally Hyperbolic Manifolds II: Application to the Restricted Three Body Problem
    Authors:
    M. J. Capiński, N. Wodka
    Academic press:
    Commun. Nonlinear Sci. Numer. Simul. (rok: 2022, tom: 111, strony: 45685), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2022.106424 - link to the publication
  14. Central configurations in spatial $n$-body problem for n=5,6 with equal masses
    Authors:
    Małgorzata Moczurad, Piotr Zgliczyński
    Academic press:
    Celestial Mechanics and Dynamical Astronomy (rok: 2020, tom: 132, strony: 56), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10569-020-09993-1 - link to the publication

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