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
Piotr Zgliczyński
room:2063
address:Łojasiewicza 6, PL-30-348 Kraków, Poland
phone:+48 12 6646667
e-mail:zgliczyn At ii.uj.edu.pl
www:http://www.ii.uj.edu.pl/~zgliczyn
Research interests:
  • qualitative theory of differential equations
  • computer assisted proofs in dynamical systems
CV light:
1988M.S. in matchematicsJagiellonian University
1990M.S. in theoretical physicsJagiellonian University
1996PhD in mathematicsJagiellonian University
2002habilitation in mathematicsJagiellonian University
2008profesor in mathematicsJagiellonian University
1998/1999NSF-NATO postdocGeorgia Institute of Technology, Atlanta, USA
1999/2000 postdocGeorgia Institute of Technology, Atlanta, USA
2000/2001visiting profesorIndiana University, Bloomington, USA
Awards and scholarships:
1998NSF-NATO postdoctoral fellowshipNSF, USA
2008Polish Prime Minister award for outstanding scientific achievementpolish goverment
Research grants:
1998-2000 Metody topologiczne w wielowymiarowych chaotycznych układach dynamicznych. Topologiczna hiperboliczność KBN, Poland
2002-2005Dynamika w niesko/nczonym wymiarze. Układy dysypatywne.KBN, Poland
2006-2009 Komputerowo wspierane dowody w dynamice równań różniczkowych zwyczajnych i cząstkowych MNiSW, Poland
2009-2012 Metody topologiczne dla rozmaitości niezmienniczych MNiSW, Poland
2012-2015 Ścisłe metody numeryczne dla równań cząstkowych dysypatywnych i równań zwyczajnych z opóźnionym argumentem NCN, Poland
2016-2018 Metody geometryczne i ścisła numeryka w układach hamiltonowskich NCN, Poland
PhD students:
  • (2005) Tomasz Kapela Choreografie w problemie N-ciał
  • (2005) Maciej Capiński Dynamika symboliczna oraz dyfuzja Arnolda w eliptycznym problemie trzech ciał
  • (2011) Zofia Mączynska Rigorous numerics for partial differential equations
  • (2011) Mikołaj Zalewski Computer-assisted proof of the existence of periodic orbits in delay differential equations
  • (2013) Jacek Cyranka Efficient algorithms for rigorous integration forward in time of dPDEs
  • (2014) Wiesław Pałka Rigorous numerics with finite elements
  • (2015) Robert Szczelina Efficient algorithms for rigorous integration forward in time of delay differetial equations
  • (2016) Aleksander Czechowski Computer assisted proofs in the slow-fast systems of ODEs
Publications:
  1. Jakub Banaśkiewicz, Piotr Kalita, Piotr Zgliczyński,
    Computer-assisted validation of the existence of periodic orbit in the Brusselator system
    Advances in Differential Equations, vol. 29, 815-862 (2024)
  2. Piotr Zgliczyński, Robert Szczelina,
    Szczelina, R., Zgliczyński, P. High-Order Lohner-Type Algorithm for Rigorous Computation of Poincaré Maps in Systems of Delay Differential Equations with Several Delays
    FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, vol. 24, 1389-1454 (2024)
  3. Jacek Kubica, Piotr Zgliczyński, Piotr Kalita,
    The pitchfork bifurcation and heteroclinic connections in the Kuramoto–Sivashinsky PDE
    Journal of Computational Dynamics, accepted for publication (2024)
  4. 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)
  5. Anna Gierzkiewicz-Pieniążek, Piotr Zgliczyński,
    From the Sharkovskii theorem to periodic orbits for the R\"ossler system
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 314, 733-751 (2022)
  6. Maciej Capiński, Marcel Guardia, Pau Martin , Tere Seara, Piotr Zgliczyński,
    Oscillatory Motions and Parabolic Manifolds at Infinity in the Planar Circular Restricted Three Body Problem
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 320, 316-370 (2022)
  7. Piotr Zgliczyński, Małgorzata Moczurad,
    Central configurations on the plane with N heavy and k light bodies
    Communications in Nonlinear Science and Numerical Simulation, vol. 114, 4991-4998 (2022)
  8. 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)
  9. Piotr Kalita, Piotr Zgliczyński,
    Rigorous FEM for 1D Burgers Equation
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 20, 853–907 (2021)
  10. Anna Gierzkiewicz-Pieniążek, Piotr Zgliczyński,
    Periodic orbits in R\"ossler system
    Communications in Nonlinear Science and Numerical Simulation, vol. 101, 105891 (2021)
  11. 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)
  12. Piotr Kalita, Piotr Zgliczyński,
    On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditions
    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION AMATHEMATICS, vol. 150, 2025-2054 (2020)
  13. Małgorzata Moczurad, Piotr Zgliczyński,
    Central configurations in spatial $n$-body problem for $n=5,6$ with equal masses
    CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 132:56 (2020)
  14. Anna Gierzkiewicz-Pieniążek, Piotr Zgliczyński,
    A computer-assisted proof of symbolic dynamics in Hyperion's rotation model
    CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, vol. 131, 33 (2019)
  15. Małgorzata Moczurad, Piotr Zgliczyński,
    Central configurations in planar $n$-body problem for $n=5,6,7$ with equal masses
    CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, vol. 131, 46 (2019)
  16. Amadeu Delshams, Adria Simon, Piotr Zgliczyński,
    Shadowing of non-transversal heteroclinic chains
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 264, 3619–-3663 (2018)
  17. Jacek Cyranka, Piotr B. Mucha, Edriss S. Titi, Piotr Zgliczyński,
    Stabilizing the long-time behavior of the forced Navier–Stokes and damped Euler systems by large mean flow
    PHYSICA D-NONLINEAR PHENOMENA, vol. 369, 18-29 (2018)
  18. Robert Szczelina, Piotr Zgliczyński,
    Algorithm for rigorous integration of Delay Differential Equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation
    FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, vol. 18, 1299-1332 (2018)
  19. Maciej Capiński, Piotr Zgliczyński,
    Beyond the Melnikov method II: Multidimensional setting
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 265, 3988-4015 (2018)
  20. Maciej Capiński, Dmitry Turaev, Piotr Zgliczyński,
    Computer assisted proof of the existence of the Lorenz attractor in the Shimizu–Morioka system
    NONLINEARITY, vol. 31, 5410 (2018)
  21. Maciej Capiński, Piotr Zgliczyński,
    Beyond the Melnikov method: a computer assisted approach
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 262, 365-417 (2017)
  22. Piotr Zgliczyński,
    Hyperbolicity and Averaging for the Srzednicki-W{'o}jcik equation
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 262, 1931-1955 (2017)
  23. Małgorzata Moczurad, Piotr Zgliczyński,
    On the Petras algorithm for verified integration of piecewise analytic functions
    JOURNAL OF COMPLEXITY, vol. 39 , 69-93 (2017)
  24. Piotr Zgliczyński,
    Topological shadowing and the Grobman-Hartman Theorem
    Topological Methods in Nonlinear Analysis, vol. 50, 757-785 (2017)
  25. Małgorzata Moczurad, Piotr Zgliczyński, Włodzimierz Zwonek,
    New lower bound estimates for quadratures of bounded analytic functions
    JOURNAL OF COMPLEXITY, vol. 34, 50–67 (2016)
  26. Aleksander Czechowski, Piotr Zgliczyński,
    Existence of periodic solutions of the FitzHugh-Nagumo equations for an explicit range of the small parameter
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 15(3), 1615-1655 (2016)
  27. Stefan Ratschan , Peter Franek, Piotr Zgliczyński,
    Quasi-decidability of a Fragment of the Analytic First-order Theory of Real Numbers
    JOURNAL OF AUTOMATED REASONING, vol. 57, 157-185 (2016)
  28. 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)
  29. Jacek Cyranka, Piotr Zgliczyński,
    Stabilizing effect of large average initial velocity in forced dissipative PDEs invariant with respect to Galilean transformations
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 261, 4648-4708 (2016)
  30. Maciej Capiński, Piotr Zgliczyński,
    Geometric proof for normally hyperbolic invariant manifolds
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 259, 6215-6286 (2015)
  31. Jacek Cyranka, Piotr Zgliczyński,
    Existence of globally attracting solutions for one-dimensional viscous Burgers equation with nonautonomous forcing - a computer assisted proof
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 14, 787-821 (2015)
  32. Piotr Zgliczyński,
    Steady states bifurcations for the Kuramoto-Sivashinsky equation - a computer assisted proof
    Journal of Computational Dynamics AIMS, 95-142 (2015)
  33. Aleksander Czechowski, Piotr Zgliczyński,
    Rigorous numerics for PDEs with indefinite tail: existence of a periodic solution of the Boussinesq equation with time-dependent forcing
    Schedae Informaticae, vol. 24, 143-158 (2015)
  34. M. Capiński, P. Zgliczyński,
    Geometric proof for normally hyperbolic invariant manifolds
    J. Diff. Eq., 259, 6215--6286 (2015)
  35. Robert Szczelina, Piotr Zgliczyński,
    A Homoclinic Orbit in a Planar Singular ODE---A Computer Assisted Proof
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 12, 1541-–1565 (2013)
  36. Maciej Capiński, Piotr Zgliczyński,
    Cone Conditions and Covering Relations for Normally Hyperbolic Invariant Manifolds
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, vol. 30, 641-670 (2011)
  37. Stefan Ratschan , Peter Franek, Piotr Zgliczyński,
    Satisfiability of Systems of Equations of Real Analytic Functions is Quasi-decidable
    LECTURE NOTES IN COMPUTER SCIENCE, vol. 6907, 315-326 (2011)
  38. Daniel Wilczak, Piotr Zgliczyński,
    C^r-Lohner algorithm
    Schedae Informaticae, vol. 20, 9-46 (2011)
  39. Maciej Capiński, Piotr Zgliczyński,
    Transition Tori in the Planar Restricted Elliptic Three Body Problem
    NONLINEARITY, vol. 24, 1395-1432 (2011)
  40. Piotr Zgliczyński,
    Rigorous Numerics for Dissipative PDEs III. An effective algorithm for rigorous integration of dissipative PDEs
    Topological Methods in Nonlinear Analysis, vol. 36, 197-262 (2010)
  41. Piotr Zgliczyński,
    Covering relations, cone conditions and stable manifold theorem
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 246, 1774-1819 (2009)
  42. Daniel Wilczak, Piotr Zgliczyński,
    Period doubling in the Rössler system - a computer assisted proof
    FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, vol. 9, 611-649 (2009)
  43. 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)
  44. Li Ming-Chia, Piotr Zgliczyński,
    On stability of forcing relations for multidimensional perturbations of interval maps
    FUNDAMENTA MATHEMATICAE, vol. 206, 241-251 (2009)
  45. Tomasz Kapela, Piotr Zgliczyński,
    A Lohner-type algorithm for control systems and ordinary differential inclusions
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, vol. 11, 365-385 (2009)
  46. Li Ming-Chia, Lyu Ming-Jiea , Piotr Zgliczyński,
    Topological entropy for multidimensional perturbations of snap-back repellers and one-dimensional maps
    NONLINEARITY, vol. 21, 2555-2567 (2008)
  47. 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)
  48. Hiroshi Kokubu, Daniel Wilczak, Piotr Zgliczyński,
    Rigorous verification of cocoon bifurcations in the Michelson system
    NONLINEARITY, vol. 20, 2147-2174 (2007)
  49. Zbigniew Galias, Piotr Zgliczyński,
    An interval method for finding fixed points and periodic orbits of infinite dimensional discrete dynamical systems
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, vol. 17, 4261-4272 (2007)
  50. Maciej Capiński, Piotr Zgliczyński,
    Covering Relations and Non-autonomous Perturbations of ODEs
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, vol. 14, 281-293 (2006)
  51. 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)
  52. Klaudiusz Wójcik, Piotr Zgliczyński,
    Topological horseshoes and delay differential equations
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, vol. 12, 827-852 (2005)
  53. Roman Srzednicki, Klaudiusz Wójcik, Piotr Zgliczyński,
    Fixed point results based on the Ważewski method
    Springer Verlag (połaczony z Kluwer Academic Publishing), 905-943 (2005)
  54. marian gidea, Piotr Zgliczyński,
    Covering relations for multidimensional dynamical systems II
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 202, 59-80 (2004)
  55. Piotr Zgliczyński,
    Rigorous numerics for dissipative Partial Differential Equations II. Periodic orbit for the Kuramoto-Sivashinsky PDE - a computer assisted proof
    FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, vol. 4, 157-185 (2004)
  56. marian gidea, Piotr Zgliczyński,
    Covering relations for multidimensional dynamical systems I
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 202, 32-58 (2004)
  57. P. Zgliczyński,
    Trapping regions and an ODE-type proof of an existence and uniqueness for Navier-Stokes equations with periodic boundary conditions on the plane
    Univ. Iag. Acta Math. 41, 89-113 (2003)
  58. Tomasz Kapela, Piotr Zgliczyński,
    The existence of simple choreographies for the N-body problem - a computer assisted proof
    NONLINEARITY, vol. 16(2), 1899-1918 (2003)
  59. P. Zgliczyński,
    On smooth dependence on initial conditions for dissipative PDEs, an ODE-type approach
    Journal of Differential Equations 195/2 271-283, 271-283 (2003)
  60. 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)
  61. Piotr Zgliczyński,
    On smooth dependence on intial conditions for dissipative PDEs, an ODE-type approach
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 195/2, 271-283 (2003)
  62. Gianni Arioli, Piotr Zgliczyński,
    Periodic, homoclinic and heteroclinic orbits for H'{e}non Heiles Hamiltonian near the critical energy level
    NONLINEARITY, vol. vol. 16, No. 5, 1833-1852 (2003)
  63. Piotr Zgliczyński,
    C^1-Lohner algorithm
    FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, vol. 2, 429-465 (2002)
  64. Klaudiusz Wójcik, Piotr Zgliczyński,
    Isolating segments, fixed point index, and symbolic dynamics. III. Applications
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 183, 262-278 (2002)
  65. Piotr Zgliczyński,
    Attracting fixed points for the Kuramoto-Sivashinsky equation
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 1, 215-235 (2002)
  66. P. Zgliczyński,
    Attracting fixed points for the Kuramoto-Sivashinsky equation - a computer assisted proof
    SIAM Journal on Applied Dynamical Systems, Vol. 1, 215-235 (2002)
  67. P. Zgliczyński,
    On periodic points for systems of weakly coupled 1-dim maps
    Nonlinear Analysis. TMA, Vol 46/7, 1039-1062 (2001)
  68. G. Arioli, P. Zgliczyński,
    Symbolic dynamics for the Henon--Heiles hamiltonian on the critical energy level
    J. Diff. Eq. 171, 173-202 (2001)
  69. M. Misiurewicz, P. Zgliczyński,
    Topological entropy for multidimensional perturbations of one dimensional maps
    Int. J. of Bifurcation and Chaos, vol. 11, 1443-1446 (2001)
  70. Klaudiusz Wójcik, Piotr Zgliczyński,
    Isolating segments, fixed point index, and symbolic dynamics. II. Homoclinic solutions.
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 172, 189-211 (2001)
  71. Konstantin Mischaikov, Piotr Zgliczyński,
    Rigorous Numerics for Partial Differential Equations: the Kuramoto-Sivashinsky equation
    FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, vol. 1, 255-288 (2001)
  72. M. Mrozek, P. Zgliczyński,
    Set arithmetic and the enclosing problem in dynamics
    Annales Pol. Math., LXXIV, 237-259 (2000)
  73. Klaudiusz Wójcik, Piotr Zgliczyński,
    Isolating segments, fixed point index, and symbolic dynamics
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 161, 245-288 (2000)
  74. Klaudiusz Wójcik, Piotr Zgliczyński,
    How to show an existence of homoclinic trajectories using topological tools?
    International Conference on Differential Equations, Vol. 1, 2 (Berlin, 1999), , World Scientific Publishing, 246-248 (2000)
  75. Klaudiusz Wójcik, Piotr Zgliczyński,
    On existence of infinitely many homoclinic solutions
    MONATSHEFTE FUR MATHEMATIK, vol. 130, 155-160 (2000)
  76. P. Zgliczyński,
    Multidimensional perturbations of one-dimensional maps and stability of Sharkovskii ordering
    Int. J. of Bifurcation and Chaos, Vol. 9, 1867-1876 (1999)
  77. P. Zgliczyński,
    Sharkovskii's Theorem for multidimensional perturbations of one-dimensional maps
    Ergodic Theory and Dynamical Systems 19, 1655-1684 (1999)
  78. P. Zgliczyński,
    Sharkovskii's Theorem for multidimensional perturbations of one-dimensional maps II
    Topological Methods in Nonlinear Analysis 14, 169-182 (1999)
  79. P. Zgliczyński,
    Symbolic dynamics for the R\"ossler folded towel map
    Conley Index Theory, Warsaw 1999, Banach Center Publications, Vol. 47, 253-258 (1999)
  80. Andrzej Szymczak , Klaudiusz Wójcik, Piotr Zgliczyński,
    On the discrete Conley index in the invariant subspace
    TOPOLOGY AND ITS APPLICATIONS, vol. 87, 105-115 (1998)
  81. Z. Galias, P. Zgliczyński,
    Computer assisted proof of chaos in the Lorenz system
    Physica D, 115, 165-188 (1998)
  82. P. Zgliczyński,
    Computer assisted proof of chaos in the Henon map and in the Rossler equations
    Nonlinearity 10, 243-252 (1997)
  83. P. Zgliczyński,
    Computer assisted proof of the horseshoe dynamics in the Henon map
    Random and Computational Dynamics, Vol. 5, 1-19 (1997)
  84. A. Sitarz, P. Zgliczyński,
    On a Matched Pair of Lie Groups for the $\kappa$-Poincar\'e in 2-Dimensions
    Mathematical Physics Electronic Journal, Vol. 2, pp. 8 (1996)
  85. P. Zgliczyński,
    Fixed point index for iterations, topological horseshoe and chaos
    Topological Methods in Nonlinear Analysis, Vol. 8, 169-177 (1996)
  86. P. Zgliczyński,
    An existence theorem for perturbation of nonlinear functional boundary value problems for ODE's
    Rivista di Matematica Pura e Applicata 19, 101-105 (1996)
  87. P. Zgliczyński,
    On dynamical System with an Integral Invariant on the Torus
    Univ. Iag. Acta Math. XXXII, 157-174 (1995)
  88. Piotr Zgliczyński,
    Abundance of homoclinic and heteroclinic orbits and rigorous bounds for the topological entropy for the Henon map
    NONLINEARITY, vol. 14, 909-932 ()
Division of Computational Mathematics, Institute of Computer Science, Łojasiewicza 6, 30-348 Kraków, Poland