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 methods and rigorous numerics in Hamiltonian dynamics

2015/19/B/ST1/01454

Keywords:

dynamical systems differential equations stability hamiltonian systems

Descriptors:

  • ST1_10: Ordinary differential equations and dynamical systems
  • ST1_12: Mathematical methods of physics
  • ST1_16: Numerical analysis

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: 4

Call: OPUS 10 - announced on 2015-09-15

Amount awarded: 313 200 PLN

Project start date (Y-m-d): 2016-07-07

Project end date (Y-m-d): 2019-07-06

Project duration:: 36 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. komputer Macbook Pro (13 716 PLN)

Information in the final report

  • Publication in academic press/journals (14)
  1. Beyond the Melnikov method II: multidimensional setting
    Authors:
    Maciej Capiński, Piotr Zgliczyński
    Academic press:
    Journal of Differential Equations (rok: 2018, tom: 265, strony: 3988-4015), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2018.05.028 - link to the publication
  2. Central configurations in the 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: pp. 56), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10569-020-09993-1 - link to the publication
  3. Persistence of normally hyperbolic invariant manifolds in the absence of rate conditions
    Authors:
    Maciej J. Capiński, Hieronim Kubica
    Academic press:
    Nonlinearity (rok: 2020, tom: 33, strony: 4967-5005), Wydawca: IOP Publishing
    Status:
    Published
    DOI:
    10.1088/1361-6544/ab8fb6 - link to the publication
  4. Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems
    Authors:
    I. Walawska and D. Wilczak
    Academic press:
    Communications in Nonlinear Science and Numerical Simulation (rok: 2019, tom: 74C, strony: 30-54), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2019.03.005 - link to the publication
  5. Beyond the Melnikov method: a computer assisted approach
    Authors:
    Maciej Capiński, Piotr Zgliczyński
    Academic press:
    J. Diff. Eq. (rok: 2017, tom: 262, strony: 365--417), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2016.09.032 - link to the publication
  6. Computer assisted proof of the existence of the Lorenz attractor in the Shimizu-Morioka system
    Authors:
    Maciej Capiński, Dimitr Turaev, Piotr Zgliczyński
    Academic press:
    Nonlinearity (rok: 2018, tom: 31, strony: 5410-5440), Wydawca: IOP
    Status:
    Published
    DOI:
    10.1088/1361-6544/aae032 - link to the publication
  7. Computer-Assisted Proof of Shil'nikov Homoclinics: With Application to the Lorenz-84 Model
    Authors:
    Maciej Capiński, Anna Wasieczko-Zając
    Academic press:
    SIAM J. of Applied Dynamical Systems (rok: 2017, tom: 16, strony: 1453–1473), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/16M1079956 - link to the publication
  8. Hyperbolicity and Averaging for the Srzednicki-Wójcik equation
    Authors:
    Piotr Zgliczynski
    Academic press:
    Journal of Differential Equation (rok: 2017, tom: 262, strony: 1931--1955), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.038 - link to the publication
  9. Systematic Computer-Assisted Proof of branches of stable elliptic periodic orbits and surrounding invariant tori
    Authors:
    Daniel Wilczak, Roberto Barrio
    Academic press:
    SIAM Journal on Applied Dynamical Systems (rok: 2017, tom: 16, strony: 1618-1649), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/17M1113254 - link to the publication
  10. Central configurations in planar $n$-body problem for $n=5,6,7$ with equal masses
    Authors:
    Małgorzata Moczurad, Piotr Zgliczyński
    Academic press:
    Celestial Mechanics and Dynamical Astronomy (rok: 2019, tom: 131, strony: pp. 46), Wydawca: Springer
    Status:
    Accepted for publication
    DOI:
    10.1007/s10569-019-9920-6 - link to the publication
  11. Rigorous KAM results around arbitrary periodic orbits for Hamiltonian systems
    Authors:
    Carles Simo, Tomasz Kapela
    Academic press:
    Nonlinearity (rok: 2017, tom: 30, strony: 965-986), Wydawca: IOP
    Status:
    Published
    DOI:
    10.1088/1361-6544/aa4ff3 - link to the publication
  12. Arnold Diffusion, Quantitative Estimates and Stochastic Behavior in the Three-Body Problem
    Authors:
    Maciej J Capinski, Marian Gidea
    Academic press:
    Communications on Pure and Applied Mathematics , Wydawca: Wiley
    Status:
    Accepted for publication
    DOI:
    brak - link to the publication
  13. A computer-assisted proof of symbolic dynamics in Hyperion's rotation
    Authors:
    Anna Gierzkiewicz, Piotr Zgliczyński
    Academic press:
    Celestial Mechanics and Dynamical Astronomy (rok: 2019, tom: 131, strony: pp. 17), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10569-019-9910-8 - link to the publication
  14. Validated Computation of Heteroclinic Sets
    Authors:
    Maciej J. Capiński, Jason D. Mireles James
    Academic press:
    SIAM J. Appl. Dyn. Syst. (rok: 2017, tom: 16, strony: 375–409), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/16M1060674 - link to the publication

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