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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Computational topological dynamics

2014/14/A/ST1/00453

Keywords:

differential equation discrete dynamical system topological invariant discrete Morse theory Conley index homology algorithms

Descriptors:

  • ST1_10: Ordinary differential equations and dynamical systems
  • ST1_6: Topology
  • 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. Marian Mrozek 

Number of co-investigators in the project: 6

Call: MAESTRO 6 - announced on 2014-06-16

Amount awarded: 2 881 752 PLN

Project start date (Y-m-d): 2015-10-01

Project end date (Y-m-d): 2022-09-30

Project duration:: 84 months (the same as in the proposal)

Project status: Project settled

Equipment purchased [PL]

  1. Stacja robocza z wyposażeniem do implementacji i testowania algorytmów. (30 000 PLN)
  2. Komputer wielkiej mocy do intensywnych, urównoleglonych obliczeń numerycznych wraz z oprzyrządowaniem ogólnym i sieciowym. (380 000 PLN)
  3. Komputer osobisty (laptop lub stacjonarny) wraz z wyposażeniem i oprogramowaniem. (50 000 PLN)

Information in the final report

  • Publication in academic press/journals (28)
  • Articles in post-conference publications (2)
  1. Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces
    Authors:
    M. Lipiński, J. Kubica, M. Mrozek, and Th. Wanner
    Academic press:
    Journal of Applied and Computational Topology (rok: 2022, tom: online, strony: 16803), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s41468-022-00102-9 - link to the publication
  2. On determining the homological Conley index of Poincare maps in autonomous systems
    Authors:
    Roman Srzednicki
    Academic press:
    Topological Methods in Nonlinear Analysis (rok: 2022, tom: 60, strony: 11810), Wydawca: Juliusz Schauder Center
    Status:
    Published
    DOI:
    10.12775/TMNA.2022.006 - link to the publication
  3. Recent advances in rigorous computation of Poincaré maps
    Authors:
    T. Kapela, D. Wilczak, P. Zgliczyński,
    Academic press:
    Communications in Nonlinear Science and Numerical Simulation (rok: 2022, tom: 110, strony: 106366), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2022.106366 - link to the publication
  4. Weak index pairs and the Conley index for discrete multivalued dynamical systems
    Authors:
    Bogdan Batko, Marian Mrozek
    Academic press:
    SIAM Journal on Applied Dynamical Systems (rok: 2016, tom: 15, strony: 1143-1162), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/15M1046691 - link to the publication
  5. Čech-Delaunay gradient flow and homology inference for self-maps
    Authors:
    Ulrich Bauer, Herbert Edelsbrunner, Grzegorz Jablonski, Marian Mrozek
    Academic press:
    J Appl. and Comput. Topology (rok: 2020, tom: 4, strony: 455-480), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s41468-020-00058-8 - link to the publication
  6. An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs
    Authors:
    Irmina Walawska, Daniel Wilczak
    Academic press:
    Applied Mathematics and Computation (rok: 2016, tom: 291, strony: 303-322), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.amc.2016.07.005 - link to the publication
  7. Connecting orbits for a singular nonautonomous real Ginzburg-Landau type equation
    Authors:
    Wilczak Daniel, Piotr Zgliczyński
    Academic press:
    SIAM Journal on Applied Dynamical Systems (rok: 2016, tom: 15, strony: 495-525), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/15M1015558 - link to the publication
  8. Distribution of stable islands within chaotic areas in the non-hyperbolic and hyperbolic regimes in the Henon-Heiles system
    Authors:
    R. Barrio, D. Wilczak
    Academic press:
    Nonlinear Dynamics (rok: 2020, tom: 102, strony: 403-416), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s11071-020-05930-x - link to the publication
  9. Systematic computer-assisted proof of branches of stable elliptic periodic orbits and surrounding invariant tori
    Authors:
    Wilczak Daniel, Barrio Roberto
    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. Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems
    Authors:
    I. Walawska, D. Wilczak
    Academic press:
    Communications in Nonlinear Science and Numerical Simulation (rok: 2019, tom: 74, strony: 30-54), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2019.03.005 - link to the publication
  11. Connection matrices in combinatorial topological dynamics
    Authors:
    Marian Mrozek and Thomas Wanner
    Academic press:
    arxiv.org (rok: 2021, ), Wydawca: arxiv.org
    Status:
    Submitted
    DOI:
    brak - link to the publication
  12. CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems
    Authors:
    T. Kapela, M. Mrozek, D. Wilczak, P. Zgliczyński
    Academic press:
    Communications in Nonlinear Science and Numerical Simulation (rok: 2021, tom: 101, strony: 45309), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2020.105578 - link to the publication
  13. Conley–Morse–Forman Theory for Combinatorial Multivector Fields on Lefschetz Complexes
    Authors:
    Marian Mrozek
    Academic press:
    Foundations of Computational Mathematics (rok: 2017, tom: 17, strony: 1585-1633), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10208-016-9330-z - link to the publication
  14. Discretization strategies for computing Conley indices and Morse decompositions of flows
    Authors:
    Konstantin Mischaikow, Marian Mrozek, Frank Weilandt
    Academic press:
    Journal of Computational Dynamics (rok: 2016, tom: 3, strony: 45307), Wydawca: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/jcd.2016001 - link to the publication
  15. Linking combinatorial and classical dynamics: Conley index and Morse decompositions
    Authors:
    B. Batko, T. Kaczynski, M. Mrozek, and Th. Wanner
    Academic press:
    Foundations of Computational Mathematics (rok: 2020, tom: 20, strony: 967–1012), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10208-020-09444-1 - link to the publication
  16. On periodic solutions in the Whitney's inverted pendulum problem
    Authors:
    R. Srzednicki
    Academic press:
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES S (rok: 2019, tom: 12, strony: 2127-2141), Wydawca: AIMS
    Status:
    Published
    DOI:
    10.3934/dcdss.2019137 - link to the publication
  17. The Morse Equation in the Conley Index Theory for Discrete Multivalued Dynamical Systems
    Authors:
    B. Batko
    Academic press:
    Journal of Dynamics and Differential Equations (rok: 2022, tom: online, strony: 45309), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10884-022-10136-3 - link to the publication
  18. Unsupervised Features Learning for Sampled Vector Fields
    Authors:
    Mateusz Juda
    Academic press:
    SIAM Journal on Applied Dynamical Systems (rok: 2020, tom: 19, strony: 2720-2736), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/19M1301758 - link to the publication
  19. Combinatorial vs. classical dynamics: Recurrence
    Authors:
    M. Mrozek, R. Srzednicki, J. Thorpe and Th. Wanner
    Academic press:
    Communications in Nonlinear Science and Numerical Simulation (rok: 2022, tom: 108, strony: 45321), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2021.106226 - link to the publication
  20. Persistence of the Conley-Morse Graph in Combinatorial Dynamical Systems
    Authors:
    T. Dey, M. Mrozek, and R. Slechta
    Academic press:
    SIAM Journal on Applied Dynamical Systems (rok: 2022, tom: 21, strony: 817-839), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/21M143162X - link to the publication
  21. Persistent Homology of Morse Decompositions in Combinatorial Dynamics
    Authors:
    Tamal K. Dey, Mateusz Juda, Tomasz Kapela, Jacek Kubica, Michal Lipinski, Marian Mrozek
    Academic press:
    SIAM Journal on Applied Dynamical Systems (rok: 2019, tom: 18, strony: 510-530), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/18M1198946 - link to the publication
  22. A Lefschetz fixed point theorem for multivalued maps of finite spaces
    Authors:
    Jonathan Ariel Barmak, Marian Mrozek, and Thomas Wanner
    Academic press:
    Mathematische Zeitschrfit (rok: 2020, tom: 294, strony: 1477-1497), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00209-019-02333-6 - link to the publication
  23. Algorithmic computation of the Conley index for multivalued maps with no continuous selector in cubical spaces
    Authors:
    Mateusz Przybylski
    Academic press:
    Schedae Informaticae (rok: 2019, tom: 28, strony: 45559), Wydawca: Uniwersytet Jagielloński
    Status:
    Published
    DOI:
    10.4467/20838476SI.19.001.14284 - link to the publication
  24. Coexistence and dynamical connections between hyperchaos and chaos in the 4D Rössler system : a computer-assisted proof
    Authors:
    Wilczak Daniel, Serrano Sergio, Barrio Roberto
    Academic press:
    SIAM Journal on Applied Dynamical Systems (rok: 2016, tom: 15, strony: 356-390), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/15M1039201 - link to the publication
  25. Conley index approach to sampled dynamics
    Authors:
    B. Batko, K. Mischaikow, M. Mrozek, M. Przybylski
    Academic press:
    SIAM Journal on Applied Dynamical Systems (rok: 2020, tom: 19, strony: 665-704), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/19M1254404 - link to the publication
  26. Creating Semiflows on Simplicial Complexes from Combinatorial Vector Fields
    Authors:
    M. Mrozek, and Th. Wanner
    Academic press:
    Journal of Differential Equations (rok: 2021, tom: 304, strony: 375-434), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.001 - link to the publication
  27. Towards a formal tie between combinatorial and classical vector field dynamics
    Authors:
    Kaczyński Tomasz, Mrozek Marian, Thomas Wanner
    Academic press:
    Journal of Computational Dynamics (rok: 2016, tom: 3, strony: 17-50), Wydawca: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/jcd.2016002 - link to the publication
  28. Weak index pairs and the Conley index for discrete multivalued dynamical systems. Part II: properties of the index
    Authors:
    Bogdan Batko
    Academic press:
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (rok: 2017, tom: 16, strony: 1587-1617), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/16M1097584 - link to the publication
  1. Tracking Dynamical Features via Continuation and Persistence
    Authors:
    T. Dey, M. Lipiński, M. Mrozek, and R. Slechta
    Conference:
    38th International Symposium on Computational Geometry (rok: 2022, ), Wydawca: Leibniz-Zentrum für Informatik, Dagstuhl Publishing
    Data:
    konferencja 2022-06-07/10
    Status:
    Published
  2. Persistence of the Conley index in combinatorial dynamical systems
    Authors:
    T. Dey, M. Mrozek, and R. Slechta
    Conference:
    36th International Symposium on Computational Geometry (rok: 2020, ), Wydawca: Leibniz-Zentrum für Informatik, Dagstuhl Publishing
    Data:
    konferencja 44007
    Status:
    Published

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