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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Topological invariants and measures of complexity in action

2014/15/B/ST1/01710

Keywords:

Nielsen number fixed point index Lefschetz number Conley index entropy rotation number applications

Descriptors:

  • ST1_10: Ordinary differential equations and dynamical systems
  • ST1_6: Topology
  • ST1_18: Control theory and optimisation

Panel:

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

Host institution :

Politechnika Gdańska, Wydział Fizyki Technicznej i Matematyki Stosowanej

woj. pomorskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

dr hab. Grzegorz Graff 

Number of co-investigators in the project: 5

Call: OPUS 8 - announced on 2014-09-15

Amount awarded: 297 960 PLN

Project start date (Y-m-d): 2015-07-15

Project end date (Y-m-d): 2018-11-14

Project duration:: 40 months (the same as in the proposal)

Project status: Project settled

Equipment purchased [PL]

  1. Nie planowano zakupu aparatury.

Information in the final report

  • Publication in academic press/journals (18)
  1. Computing algebraic transfer entropy and coupling directions via transcripts
    Authors:
    José M. Amigó, Roberto Monetti, Beata Graff, Grzegorz Graff
    Academic press:
    Chaos (rok: 2016, tom: 11, strony: 1-12 nr id. 113115), Wydawca: American Institute of Physics
    Status:
    Published
    DOI:
    10.1063/1.4967803 - link to the publication
  2. Periodic Points for Sphere Maps Preserving Monopole Foliations
    Authors:
    Grzegorz Graff, Michał Misiurewicz, Piotr Nowak-Przygodzki
    Academic press:
    Qualitative Theory of Dynamical Systems (rok: 2019, tom: 18 no. 2, strony: 533-546), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s12346-018-0298-8 - link to the publication
  3. When a smooth self-map of a semi-simple Lie group can realize the least number of periodic points
    Authors:
    Jerzy Jezierski
    Academic press:
    SCIENCE CHINA Mathematics (rok: 2017, tom: 60 no 9, strony: 1579–1590), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11425-016-9099-9 - link to the publication
  4. Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos
    Authors:
    Jonathan E. Rubin, Justyna Signerska-Rynkowska, Jonathan D. Touboul, Alexandre Vidal
    Academic press:
    Discrete and Continuous Dynamical System - B (rok: 2017, tom: 22 no 10, strony: 3967-4002), Wydawca: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/dcdsb.2017204 - link to the publication
  5. A sufficient condition for the realizability of the least number of periodic points of a smooth map
    Authors:
    Jerzy Jezierski
    Academic press:
    Journal of Fixed Point Theory and Applications (rok: 2016, tom: 18, strony: 609–626), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11784-016-0311-2 - link to the publication
  6. DYNAMICS OF FIELD LINE MAPPINGS IN MAGNETIC FLUX TUBES
    Authors:
    Grzegorz Graff, Justyna Rynkowska-Signerska
    Academic press:
    Mathematical Physics, Analysis and Geometry (rok: 2018, tom: 21 no. 3,, strony: Art. 26, 18pp), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11040-018-9284-2. - link to the publication
  7. FIXED POINT INDICES OF ITERATES OF A LOW-DIMENSIONAL DIFFEOMORPHISM AT A FIXED POINT WHICH IS AN ISOLATED INVARIANT SET
    Authors:
    Grzegorz Graff
    Academic press:
    Archiv der Mathematik (rok: 2018, tom: 110 no 6, strony: 617–627), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00013-018-1180-2 - link to the publication
  8. Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
    Authors:
    Grzegorz Graff, Jerzy Jezierski
    Academic press:
    Geometria Dedicata (rok: 2017, tom: 187 no 1, strony: 241–258), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10711-016-0199-4 - link to the publication
  9. Analysis of interspike-intervals for the general class of integrate-and-fire models with periodic drive
    Authors:
    Justyna Signerska-Rynkowska
    Academic press:
    Mathematical Modelling And Analysis (rok: 2015, tom: 20, strony: 529-551), Wydawca: Taylor & Francis
    Status:
    Published
    DOI:
    10.3846/13926292.2015.1085459 - link to the publication
  10. Integrate-and-fire models with an almost periodic input function
    Authors:
    Piotr Kasprzak, Adam Nawrocki, Justyna Signerska-Rynkowska
    Academic press:
    Journal of Differential Equations (rok: 2018, tom: 264, strony: 2495–2537), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.025 - link to the publication
  11. Periodic expansion in determining minimal sets of Lefschetz periods for Morse-Smale diffeomorphisms
    Authors:
    Grzegorz Graff, Małgorzata Lebiedź, Adrian Myszkowski
    Academic press:
    Journal of Fixed Point Theory and Applications (rok: 2019, tom: 21 no. 2, strony: Art 47, 21pp), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11784-019-0680-4 - link to the publication
  12. Periodic points of latitudinal maps of the $m$-dimensional sphere
    Authors:
    Grzegorz Graff, Michał Misiurewicz, Piotr Nowak-Przygodzki
    Academic press:
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS (rok: 2016, tom: 36 (11), strony: 6187 - 6199), Wydawca: American Insitute of mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/dcds.2016070 - link to the publication
  13. SHUB'S CONJECTURE FOR SMOOTH LONGITUDINAL MAPS OF S^m
    Authors:
    GRZEGORZ GRAFF, MICHAŁ MISIUREWICZ, PIOTR NOWAK-PRZYGODZKI
    Academic press:
    Journal of Difference Equations and Applications (rok: 2018, tom: 24 no 7, strony: 1044–1054), Wydawca: Taylor & Francis
    Status:
    Published
    DOI:
    10.1080/10236198.2018.1449840 - link to the publication
  14. The least number of 2-periodic points of a smooth self-map of S^2 of degree 2 equals 2
    Authors:
    Jerzy Jezierski
    Academic press:
    Journal of Fixed Point Theory and Applications (rok: 2019, tom: 21 no. 1, strony: Art 14, 13pp), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11784-018-0651-1 - link to the publication
  15. Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-mode oscillations
    Authors:
    Jonathan E. Rubin, Justyna Signerska-Rynkowska, Jonathan D. Touboul, Alexandre Vidal
    Academic press:
    Discrete and Continuous Dynamical System - B (rok: 2017, tom: 22 no 10, strony: 4003-4039), Wydawca: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/dcdsb.2017205 - link to the publication
  16. DETECTING COUPLING DIRECTIONS WITH TRANSCRIPT MUTUAL INFORMATION: A COMPARATIVE STUDY
    Authors:
    Jose M. Amigo, Beata Graff,Grzegorz Graff, Roberto Monetti, Katarzyna Tessmer
    Academic press:
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B (rok: 2019, tom: 24 no. 8, strony: 4079–4097), Wydawca: AMERICAN INSTITUTE OF MATHEMATICAL SCIENCES-AIMS,
    Status:
    Published
    DOI:
    10.3934/dcdsb.2019051 - link to the publication
  17. GENERATING SEQUENCES OF LEFSCHETZ NUMBERS OF ITERATES
    Authors:
    GRZEGORZ GRAFF, MAŁGORZATA LEBIEDŹ, PIOTR NOWAK-PRZYGODZKI
    Academic press:
    Monatshefte für Mathematik (rok: 2019, tom: 188 no. 3, strony: 511-525), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00605-018-1193-8 - link to the publication
  18. Self-maps of S^2 homotopic to a smooth map with a single n-periodic point
    Authors:
    Jerzy Jezierski
    Academic press:
    Acta Mathematica Sinica (rok: 2017, tom: 33 no 8, strony: 1073–1082), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10114-017-6120-8 - link to the publication

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