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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Diffusion in Hamiltonian systems.

2012/05/B/ST1/00355

Keywords:

Hamiltonian systems Arnold diffusion invariant tori normally hyperbolic manifolds Melnikov method homo/heteroclinic connections

Descriptors:

  • ST1_10: Ordinary differential equations and dynamical systems

Panel:

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

Host institution :

Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie, Wydział Matematyki Stosowanej

woj. małopolskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

dr Maciej Capiński 

Number of co-investigators in the project: 1

Call: OPUS 3 - announced on 2012-03-15

Amount awarded: 51 900 PLN

Project start date (Y-m-d): 2013-02-06

Project end date (Y-m-d): 2016-02-05

Project duration:: 36 months (the same as in the proposal)

Project status: Project settled

Equipment purchased [PL]

  1. 15-calowy, czterordzeniowy, Apple MacBook Pro (8 700 PLN)

Information in the final report

  • Publication in academic press/journals (5)
  1. Geometric Proof of Strong Stable/Unstable Manifolds, with Application to the Restricted Three Body Problem
    Authors:
    Maciej J. Capiński, Anna Wasieczko
    Academic press:
    Topological Methods in Nonlinear Analysis (rok: 2015, tom: 46, strony: 363–399), Wydawca: Juliusz P. Schauder Center for Nonlinear Studies
    Status:
    Published
    DOI:
    10.12775/TMNA.2015.051 - link to the publication
  2. Beyond the Melnikov method: a computer assisted approach
    Authors:
    Maciej J. Capiński, Piotr Zgliczyński
    Academic press:
    Foundations of Computational Mathematics (rok: 2017, tom: 262, strony: 365-417), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2016.09.032 - link to the publication
  3. Geometric proof for normally hyperbolic invariant manifolds
    Authors:
    Maciej J. Capiński, Piotr Zgliczyński
    Academic press:
    Journal of Differential Equations (rok: 2015, tom: 259, strony: 6215–6286), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2015.07.020 - link to the publication
  4. Validated Computation of Heteroclinic Sets
    Authors:
    Maciej J. Capiński, Jason D. Mireles James
    Academic press:
    SIAM Journal on Applied Dynamical Systems (SIADS) (rok: 2017, tom: 16, strony: 375–409), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/16M1060674 - link to the publication
  5. Arnold diffusion in the planar elliptic restricted three-body problem: mechanism and numerical verification
    Authors:
    Maciej J. Capiński, Marian Gidea, Rafael de la Llave
    Academic press:
    Nonlinearity (rok: 2017, tom: 30, strony: 329-360), Wydawca: IOPscience
    Status:
    Published
    DOI:
    10.1088/1361-6544/30/1/329 - link to the publication

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