Jagiellonian University
Institute of Computer Science
and Computational Mathematics

The Home Page Of Daniel Wilczak

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Coauthors:


Papers and preprints:

  1. D. Wilczak, P. Zgliczyński,
    Symbolic dynamics for Kuramoto-Sivashinsky PDE on the line - a computer-assisted proof

  2. 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), 1618-1649 (2017).

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

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

    Auxiliary materials:
    C++ sources.

  4. 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), 495-525 (2016).

    Auxiliary materials:
    C++ sources.

  5. 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, 356-390 (2016).

    Auxiliary materials:
    C++ sources.
    Data.

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

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

  8. 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, 1263-1283 (2010).

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

  9. 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, 1632-1663 (2009).


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


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


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


  13. 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).

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


  15. 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, 629-652, (2007).


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


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

  18. 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, 561-576, (2005).


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


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


  21. 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, No.1, 37-75, (2003).


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

    Applet which shows the dynamics of the Rössler map.