Jagiellonian University
Institute of Computer Science
and Computational Mathematics

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Papers and preprints:

  1. D. Wilczak, P. Zgliczyński,
    A rigorous C1-algorithm for integration of dissipative PDEs based on automatic differentiation and the Taylor method
    in preparation


  2. J.B. van den Berg, M. Capiński, J.D. Mireles James, W. Tucker, D. Wilczak,
    Computer assisted proofs in dynamical systems
    Communications in Nonlinear Science and Numerical Simulation vol. 118 (2023), 106998

  3. T. Kapela, D. Wilczak, P. Zgliczyński,
    Recent advances in rigorous computation of Poincarè maps
    Communications in Nonlinear Science and Numerical Simulation, Volume 110, July 2022, 106366.
    https://doi.org/10.1016/j.cnsns.2022.106366
    download article

  4. T. Kapela, M. Mrozek, D. Wilczak, P. Zgliczyński,
    CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems
    Communications in Nonlinear Science and Numerical Simulation, Volume 101, October 2021, 105578.
    https://doi.org/10.1016/j.cnsns.2020.105578
    download preprint

  5. R. Barrio, D. Wilczak,
    Distribution of stable islands within chaotic areas in the non-hyperbolic and hyperbolic regimes in the Henon-Heiles system
    Nonlinear Dynamics, 102 (2020), 403-416.
    download article

  6. D. Wilczak, P. Zgliczyński,
    A geometric method for infinite-dimensional chaos: symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line
    Journal of Differential Equations, Vol. 269 No. 10 (2020), 8509-8548.
    download article

    Supplementary material:
    Supplement as a single archive.
    Description of the program.

  7. I. Walawska, D. Wilczak,
    Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems
    Communications in Nonlinear Science and Numerical Simulation, Vol. 74C (2019), 30-54.
    download preprint

    Supplementary material:
    Supplement as a single archive.
    Description of the program.

  8. D. Wilczak, R. Barrio,
    Systematic Computer-Assisted Proof of branches of stable elliptic periodic orbits and surrounding invariant tori
    SIAM Journal on Applied Dynamical Systems, Vol. 16 No. 3 (2017), 1618-1649.
    download preprint

    Auxiliary materials:
    A movie (36 MB) - phase portrait of the Michelson system.
    C++ sources and installation instruction.

  9. I. Walawska, D. Wilczak,
    An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs
    Applied Mathematics and Computation, Vol. 291C (2016), 303-322.
    download article

    Auxiliary materials:
    C++ sources.

  10. D. Wilczak, P. Zgliczyński,
    Connecting orbits for a singular nonautonomous real Ginzburg-Landau type equation.
    SIAM Journal on Applied Dynamical Systems, Vol. 15 No. 1 (2016), 495-525.
    download article

    Auxiliary materials:
    C++ sources.

  11. D. Wilczak, S. Serrano, R. Barrio,
    Coexistence and dynamical connections between hyperchaos and chaos in the 4D Rössler system: a Computer-assisted proof
    SIAM Journal on Applied Dynamical Systems, Vol. 15, No. 1 (2016), 356-390.
    download article

    Auxiliary materials:
    C++ sources.
    Data.

  12. R. Barrio, M.A. Martinez, S. Serrano, D. Wilczak,
    When chaos meets hyperchaos: 4D Rössler model
    Physics Letters A, Vol. 379, No. 38 (2015), 2300-2305.
    download preprint

  13. D. Wilczak, P. Zgliczyński,
    Cr-Lohner algorithm,
    Schedae Informaticae, Vol. 20 (2011), 9-46.

  14. D. Wilczak,
    Uniformly hyperbolic attractor of the Smale-Williams type for a Poincaré map in the Kuznetsov system,
    SIAM Journal on Applied Dynamical Systems, Vol. 9, No. 4 (2010), 1263-1283.
    download article

    Auxiliary materials:
    C++ sources and installation instruction.
    Evolution of a toroidal domain by the Kuznetsov flow - animation, 3.2 MB.

  15. D. Wilczak, P. Zgliczyński,
    Computer assisted proof of the existence of homoclinic tangency for the Henon map and for the forced-damped pendulum,
    SIAM Journal on Applied Dynamical Systems, Vol. 8, No. 4 (2009), 1632-1663.
    download article

    C++ sources and installation instruction.

  16. W. Tucker, D. Wilczak,
    A rigorous lower bound for the stability regions of the quadratic map,
    Physica D, Vol. 238, No. 18 (2009), 1923-1936.
    download preprint

    C++ sources and installation instruction.

  17. D. Wilczak, P. Zgliczyński,
    Period doubling in the Rössler system - a computer assisted proof,
    Foundations of Computational Mathematics, Vol. 9, No. 5 (2009), 611-649.
    download preprint

    C++ sources and installation instruction.

  18. D. Wilczak,
    Abundance of heteroclinic and homoclinic orbits for the hyperchaotic Rössler system,
    Discrete and Continuous Dynamical System - Series B, Vol. 11, No. 4 (2009). 1039-1055.
    download preprint

    C++ sources and installation instruction.

  19. D. Wilczak,
    Rigorous numerics for homoclinic dynamics,
    The Joint Conference of ASCM 2009 and MACIS 2009, 301-305, COE Lect. Note, 22, Kyushu Univ. Fac. Math., Fukuoka, (2009).
    download article

  20. H. Kokubu, D. Wilczak and P. Zgliczyński,
    Rigorous verification of cocoon bifurcations in the Michelson system,
    Nonlinearity 20, No.9 (2007), 2147-2174.
    download preprint

    C++ sources and installation instruction.

  21. D. Wilczak, P. Zgliczyński,
    Topological method for symmetric periodic orbits for maps with a reversing symmetry,
    Discrete and Continuous Dynamical Systems - Series A, Vol.17, No.3 (2007), 629-652.
    download preprint

    C++ sources and installation instruction.

  22. D. Wilczak,
    The existence of Shilnikov homoclinic orbits in the Michelson system: a computer assisted proof.
    Foundations of Computational Mathematics, Vol.6, No.4 (2006), 495-535.
    download preprint

    C++ sources and installation instruction.

  23. D. Wilczak,
    Symmetric homoclinic solutions to the periodic orbits in the Michelson system,
    Topological Methods in Nonlinear Analysis, Vol. 28, No. 1 (2006), 155-170.
    download article

  24. D. Wilczak, P. Zgliczyński,
    Heteroclinic Connections between Periodic Orbits in Planar Circular Restricted Three Body Problem - part II,
    Communications in Mathematical Physics, Vol. 259, No.3 (2005), 561-576.
    download preprint

    C++ sources and installation instruction.

  25. D. Wilczak,
    Symmetric heteroclinic connections in the Michelson system - a computer assisted proof,
    SIAM Journal on Applied Dynamical Systems, Vol.4, No.3 (2005), 489-514.
    download article

    C++ sources and installation instruction.

  26. D. Wilczak,
    Chaos in the Kuramoto-Sivashinsky equations - a computer assisted proof,
    Journal of Differential Equations, Vol.194 (2003), 433-459.
    download preprint

    C++ sources and installation instruction.

  27. D.Wilczak, P. Zgliczyński,
    Heteroclinic Connections between Periodic Orbits in Planar Circular Restricted Three Body Problem - A Computer Assisted Proof,
    Communications in Mathematical Physics, Vol.234 (2003), No.1, 37-75.
    download preprint

    C++ sources and installation instruction.

  28. D. Wilczak,
    Computer assisted proof of chaotic dynamics in the Rössler map,
    Topological Methods in Nonlinear Analysis, Vol.18 (2001), 183-190.
    download preprint

    Applet which shows the dynamics of the Rössler map.