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Computational topological dynamics

2014/14/A/ST1/00453

Keywords

Descriptors

  • ST1_10: Równania różniczkowe zwyczajne i układy dynamiczne
  • ST1_6: Topologia
  • ST1_16: Analiza numeryczna i obliczenia naukowe

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

Voivodeship: 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
2015-10-01
Project end date
2022-09-30
Project duration
84 months (the same as in the proposal)
Project status
Project settled

Equipment purchased [PL]

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

Information in the final report

Publication in academic press/journals (27)

  1. 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 (year: 2021, volume: 101, pages: 46040), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2020.105578 – link to the publication

  2. Creating Semiflows on Simplicial Complexes from Combinatorial Vector Fields

    Authors:
    M. Mrozek, and Th. Wanner
    Academic press:
    Journal of Differential Equations (year: 2021, volume: 304, pages: 375-434), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2021.10.001 – link to the publication

  3. 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 (year: 2022, volume: online, pages: 16803), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s41468-022-00102-9 – link to the publication

  4. 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 (year: 2022, volume: 21, pages: 817-839), Publisher: SIAM
    Status:
    Published
    DOI:
    10.1137/21M143162X – link to the publication

  5. The Morse Equation in the Conley Index Theory for Discrete Multivalued Dynamical Systems

    Authors:
    B. Batko
    Academic press:
    Journal of Dynamics and Differential Equations (year: 2022, volume: online, pages: 46040), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s10884-022-10136-3 – link to the publication

  6. Recent advances in rigorous computation of Poincaré maps

    Authors:
    T. Kapela, D. Wilczak, P. Zgliczyński,
    Academic press:
    Communications in Nonlinear Science and Numerical Simulation (year: 2022, volume: 110, pages: 106366), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2022.106366 – link to the publication

  7. Combinatorial vs. classical dynamics: Recurrence

    Authors:
    M. Mrozek, R. Srzednicki, J. Thorpe and Th. Wanner
    Academic press:
    Communications in Nonlinear Science and Numerical Simulation (year: 2022, volume: 108, pages: 46052), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2021.106226 – link to the publication

  8. On determining the homological Conley index of Poincare maps in autonomous systems

    Authors:
    Roman Srzednicki
    Academic press:
    Topological Methods in Nonlinear Analysis (year: 2022, volume: 60, pages: 11810), Publisher: Juliusz Schauder Center
    Status:
    Published
    DOI:
    10.12775/TMNA.2022.006 – link to the publication

  9. Conley–Morse–Forman Theory for Combinatorial Multivector Fields on Lefschetz Complexes

    Authors:
    Marian Mrozek
    Academic press:
    Foundations of Computational Mathematics (year: 2017, volume: 17, pages: 1585-1633), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s10208-016-9330-z – link to the publication

  10. Towards a formal tie between combinatorial and classical vector field dynamics

    Authors:
    Kaczyński Tomasz, Mrozek Marian, Thomas Wanner
    Academic press:
    Journal of Computational Dynamics (year: 2016, volume: 3, pages: 17-50), Publisher: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/jcd.2016002 – link to the publication

  11. 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 (year: 2017, volume: 16, pages: 1618-1649), Publisher: SIAM
    Status:
    Published
    DOI:
    10.1137/17M1113254 – link to the publication

  12. 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 (year: 2017, volume: 16, pages: 1587-1617), Publisher: SIAM
    Status:
    Published
    DOI:
    10.1137/16M1097584 – link to the publication

  13. Discretization strategies for computing Conley indices and Morse decompositions of flows

    Authors:
    Konstantin Mischaikow, Marian Mrozek, Frank Weilandt
    Academic press:
    Journal of Computational Dynamics (year: 2016, volume: 3, pages: 46038), Publisher: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/jcd.2016001 – link to the publication

  14. 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 (year: 2016, volume: 15, pages: 356-390), Publisher: SIAM
    Status:
    Published
    DOI:
    10.1137/15M1039201 – link to the publication

  15. 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 (year: 2016, volume: 291, pages: 303-322), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.amc.2016.07.005 – link to the publication

  16. 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 (year: 2016, volume: 15, pages: 1143-1162), Publisher: SIAM
    Status:
    Published
    DOI:
    10.1137/15M1046691 – link to the publication

  17. Connecting orbits for a singular nonautonomous real Ginzburg-Landau type equation

    Authors:
    Wilczak Daniel, Piotr Zgliczyński
    Academic press:
    SIAM Journal on Applied Dynamical Systems (year: 2016, volume: 15, pages: 495-525), Publisher: SIAM
    Status:
    Published
    DOI:
    10.1137/15M1015558 – link to the publication

  18. 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 (year: 2019, volume: 74, pages: 30-54), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2019.03.005 – link to the publication

  19. 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 (year: 2020, volume: 102, pages: 403-416), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s11071-020-05930-x – link to the publication

  20. Conley index approach to sampled dynamics

    Authors:
    B. Batko, K. Mischaikow, M. Mrozek, M. Przybylski
    Academic press:
    SIAM Journal on Applied Dynamical Systems (year: 2020, volume: 19, pages: 665-704), Publisher: SIAM
    Status:
    Published
    DOI:
    10.1137/19M1254404 – link to the publication

  21. 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 (year: 2020, volume: 4, pages: 455-480), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s41468-020-00058-8 – link to the publication

  22. Unsupervised Features Learning for Sampled Vector Fields

    Authors:
    Mateusz Juda
    Academic press:
    SIAM Journal on Applied Dynamical Systems (year: 2020, volume: 19, pages: 2720-2736), Publisher: SIAM
    Status:
    Published
    DOI:
    10.1137/19M1301758 – link to the publication

  23. A Lefschetz fixed point theorem for multivalued maps of finite spaces

    Authors:
    Jonathan Ariel Barmak, Marian Mrozek, and Thomas Wanner
    Academic press:
    Mathematische Zeitschrfit (year: 2020, volume: 294, pages: 1477-1497), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00209-019-02333-6 – link to the publication

  24. Algorithmic computation of the Conley index for multivalued maps with no continuous selector in cubical spaces

    Authors:
    Mateusz Przybylski
    Academic press:
    Schedae Informaticae (year: 2019, volume: 28, pages: 46289), Publisher: Uniwersytet Jagielloński
    Status:
    Published
    DOI:
    10.4467/20838476SI.19.001.14284 – link to the publication

  25. On periodic solutions in the Whitney's inverted pendulum problem

    Authors:
    R. Srzednicki
    Academic press:
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES S (year: 2019, volume: 12, pages: 2127-2141), Publisher: AIMS
    Status:
    Published
    DOI:
    10.3934/dcdss.2019137 – link to the publication

  26. 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 (year: 2020, volume: 20, pages: 967–1012), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s10208-020-09444-1 – link to the publication

  27. 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 (year: 2019, volume: 18, pages: 510-530), Publisher: SIAM
    Status:
    Published
    DOI:
    10.1137/18M1198946 – link to the publication

Articles in post-conference publications (2)

  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 (year: 2022, pages: 35:1-35:17), Publisher: Leibniz-Zentrum für Informatik, Dagstuhl Publishing
    Date:
    conference 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 (year: 2020, pages: 37:1–37:17), Publisher: Leibniz-Zentrum für Informatik, Dagstuhl Publishing
    Date:
    conference 44007
    Status:
    Published

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