Seminars:
Computational mathematics Thu 16:15-17:45
room 1016 Image and Data Processing Tue 11:30-13:00
room 1146 Differential equations and related issues Fri 12:15-13:45
room 1016 Partial differential equations Tue 12:15-13:45
room 1016
Daniel Wilczak, PhD
room:2060
address:Łojasiewicza 6, PL-30-348 Kraków, Poland
e-mail:Daniel.Wilczak@uj.edu.pl
www:http://www.ii.uj.edu.pl/~wilczak
Research interests:
  • qualitative theory of differential equations
  • computer assisted proofs in dynamical systems
  • GPU computing
CV light:
1999M.S. in mathematicsJagiellonian University
2003PhD in computer scienceJagiellonian University
2008 Apr.- 2009 Aug.postdocUniversity of Bergen, Norway
2009 Sept. - 2010 Aug.visiting researcherUniversity of Uppsala, Sweden
2011habilitation in computer scienceJagiellonian University
2011-2017ProfessorNowy Sącz WSB-NLU
2012 Sept. - 2013 Sept.v-ce directorInstitute of Computer Science, Jagiellonian University
2019 - presentProfessorInstitute of Computer Science and Computational Mathematics, Jagiellonian University
Awards and scholarships:
2003annual scholarschip for PhD studentsPolish Academy of Sciences
2006annual national scholarship for young scientistsFoundation for Polish Science
2007annual national scholarship for young scientists - continuationFoundation for Polish Science
2011triennial scholarship for outstanding young scientistsPolish Ministry of Science and Education
Research grants:
2011-2012Parallel and distributed algorithms in Computational Mathematics (head)Polish Ministry of Science and Education
PhD students:
  • (2019) Irmina Walawska Algorytmy ścisłego całkowania równań wariacyjnych i ich zastosowania do badania bifurkacji rozwiązań okresowych w Kołowym Ograniczonym Problemie Trzech Ciał
Publications:
  1. Daniel Wilczak, Maciej Capiński, Warwick Tucker, Jason D. Mireles James, Jan Bouwe van den Berg,
    Computer assisted proofs in dynamical systems
    Communications in Nonlinear Science and Numerical Simulation, vol. 118, 106998 (2023)
  2. Tomasz Kapela, Daniel Wilczak, Piotr Zgliczyński,
    Recent advances in a rigorous computation of Poincaré maps
    Communications in Nonlinear Science and Numerical Simulation, vol. 110, 106366 (2022)
  3. Tomasz Kapela, Marian Mrozek, Daniel Wilczak, Piotr Zgliczyński,
    CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems
    Communications in Nonlinear Science and Numerical Simulation, vol. 101, 105578 (2021)
  4. Roberto Barrio, Daniel Wilczak,
    Distribution of stable islands within chaotic areas in the non-hyperbolic and hyperbolic regimes in the Henon-Heiles system
    NONLINEAR DYNAMICS, vol. 102, 403-416 (2020)
  5. Daniel Wilczak, Piotr Zgliczyński,
    A geometric method for infinite-dimensional chaos: Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 269, 8509-8548 (2020)
  6. Irmina Walawska, Daniel 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, 30-54 (2019)
  7. Roberto Barrio, Daniel Wilczak,
    Systematic Computer-Assisted Proof of Branches of Stable Elliptic Periodic Orbits and Surrounding Invariant Tori
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 16, 1618-1649 (2017)
  8. Roberto Barrio, Sergio Serrano, Daniel Wilczak,
    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, 356-390 (2016)
  9. Daniel Wilczak, Piotr Zgliczyński,
    Connecting Orbits for a Singular Nonautonomous Real Ginzburg--Landau Type Equation
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 15, 495-525 (2016)
  10. Irmina Walawska, Daniel Wilczak,
    An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs
    APPLIED MATHEMATICS AND COMPUTATION, vol. 291, 303-322 (2016)
  11. Roberto Barrio, María Angeles Martinez, Sergio Serrano, Daniel Wilczak,
    When chaos meets hyperchaos: 4D Rössler model
    PHYSICS LETTERS A, vol. 379, 2300-2305 (2015)
  12. Daniel Wilczak, Piotr Zgliczyński,
    C^r-Lohner algorithm
    Schedae Informaticae, vol. 20, 9-46 (2011)
  13. Daniel 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, 1263-1283 (2010)
  14. Daniel Wilczak, Piotr 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, 1632-1663 (2009)
  15. Daniel Wilczak,
    Rigorous numerics for homoclinic dynamics
    The Joint Conference of ASCM 2009 and MACIS 2009, COE Lect. Note, 22, Kyushu Univ. Fac. Math., Fukuoka, 301-305 (2009)
  16. Daniel Wilczak,
    Abundance of heteroclinic and homoclinic orbits for the hyperchaotic Rössler system
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, vol. 11, 1039-1055 (2009)
  17. Daniel Wilczak, Piotr Zgliczyński,
    Period doubling in the Rössler system - a computer assisted proof
    FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, vol. 9, 611-649 (2009)
  18. Warwick Tucker, Daniel Wilczak,
    A rigorous lower bound for the stability regions of the quadratic map
    PHYSICA D-NONLINEAR PHENOMENA, vol. 238, 1923-1936 (2009)
  19. Hiroshi Kokubu, Daniel Wilczak, Piotr Zgliczyński,
    Rigorous verification of cocoon bifurcations in the Michelson system
    NONLINEARITY, vol. 20, 2147-2174 (2007)
  20. Daniel Wilczak, Piotr Zgliczyński,
    Topological method for symmetric periodic orbits for maps with a reversing symmetry
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, vol. 17, 629-652 (2007)
  21. Daniel Wilczak,
    Symmetric homoclinic solutions to the periodic orbits in the Michelson system
    Topological Methods in Nonlinear Analysis, vol. 28, 155-170 (2006)
  22. Daniel Wilczak,
    The existence of Shilnikov homoclinic orbits in the Michelson system: a computer assisted proof
    FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, vol. 6, 495-535 (2006)
  23. Daniel Wilczak,
    Symmetric heteroclinic connections in the Michelson system - a computer assisted proof
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 4, 489-514 (2005)
  24. Daniel Wilczak, Piotr Zgliczyński,
    Heteroclinic Connections between Periodic Orbits in Planar Circular Restricted Three Body Problem - part II
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 259, 561-576 (2005)
  25. Daniel Wilczak,
    Chaos in the Kuramoto-Sivashinsky equations - a computer assisted proof
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 194, 433-459 (2003)
  26. Daniel Wilczak, Piotr Zgliczyński,
    Heteroclinic Connections between Periodic Orbits in Planar Circular Restricted Three Body Problem - A Computer Assisted Proof
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 234, 37-75 (2003)
  27. Daniel Wilczak,
    Computer assisted proof of chaotic dynamics in the Rössler map
    Topological Methods in Nonlinear Analysis, vol. 18, 183-190 (2001)
Division of Computational Mathematics, Institute of Computer Science, Łojasiewicza 6, 30-348 Kraków, Poland