Seminars:
Computational mathematics Thu 16:15-17:45
room 1016
Image recognition Thu 14:15-15:45
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

Conferences:
2016-04Computation in Dynamics, ICERM Brown University Melnikov-type method for splitting of separatrices for an explicit range of small parameter Providence - USA
2015-09Mathsflows 2015, UW, Univ. Paris-Est The effect of fast movement in dissipative PDEs with the forcing term Porquerolles - Francja
2015-06Global Dynamics in Hamiltonian Systems, UPC Barcelona Melnikov-type method for splitting of separatrices for an explicit range of small parameter Girona - Hiszpania
2015-04Information Based Complexity, IMPAN New lower bound estimates for quadratures of bounded analytic functions Będlewo - Polska
2014-09Rigorously Verified Computing for Infinite Dimensional Nonlinear Dynamics, CRC Geometric methods in the integration of evolutionary problems in infinite dimension Banff - Kanada
2014-0710th AIMS Conference on Dynamical Systems, Differential Equations and Applications, AIMS Geometric Proof of the Normally Hyperbolic Invariant Manifold Theorem Madryt - Hiszpania

Publications:
  • M. Capiński, P. Zgliczyński,
    Geometric proof for normally hyperbolic invariant manifolds
    J. Diff. Eq., (2016 ?)
  • A. Czechowski, P. Zgliczyński,
    Existence of Periodic Solutions of the FitzHugh-Nagumo Equations for An Explicit Range of the Small Parameter
    SIAM Journal on Applied Dynamical Systems, 15, 1615-1655 (2016)
  • J. Cyranka, P. Zgliczyński,
    Stabilizing effect of large average initial velocity in forced dissipative PDEs invariant with respect to Galilean transformations
    J. Diff. Eq., 261, 4648--4708 (2016)
  • D. Wilczak, P. Zgliczyński,
    Connecting orbits for a singular nonautonomous real Ginzburg-Landau type equation
    SIAM Journal on Applied Dynamical Systems, 15, 495-525 (2016)
  • M. Moczurad, W. Zwonek, P. Zgliczyński,
    New lower bound estimates for quadratures of bounded analytic functions
    Journal of Complexity, 34 , 50-–67 (2016)
  • P. Franek, S. Ratschan, P. Zgliczyński,
    Quasi-decidability of a Fragment of the Analytic First-order Theory of Real Numbers
    Journal of Automated Reasoning 57, 157-–185 (2016)
  • J. Cyranka, P. 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)
  • A. Czechowski, P. Zgliczyński,
    Rigorous numerics for PDEs with indefinite tail: existence of a periodic solution of the Boussinesq equation with time-dependent forcing
    Schedae Informaticae, vol 14, 143--158 (2015)
  • Piotr Zgliczyński,
    Steady states bifurcations for the Kuramoto-Sivashinsky equation - a computer assisted proof
    , 95-142 (2015)
  • R. Szczelina, P. Zgliczyński,
    A homoclinic orbit in a planar singular ODE - a computer assisted proof
    SIAM Journal on Applied Dynamical Systems, vol 12, 1541-1565 (2013)
  • P. Franek, S. Ratschan, P. Zgliczyński,
    Satisfiability of Systems of Equations of Real Analytic Functions is Quasi-decidable
    Mathematical Foundations of Computer Science 2011, Lecture Notes in Computer Science, vol. 6907, 315-326 (2011)
  • M. Capiński, P. Zgliczyński,
    Cone Conditions and Covering Relations for Normally Hyperbolic Invariant Manifolds
    Discrete Cont. Dyn. Sys. A 30, 641--670 (2011)
  • M. Capiński, P. Zgliczyński,
    Transition Tori in the Planar Restricted Elliptic Three Body Problem
    Nonlinearity 24, 1395-1432 (2011)
  • Daniel Wilczak, Piotr Zgliczyński,
    C^r-Lohner algorithm
    SCHEDAE INFORMATICAE , 9-46 (2011)
  • P. Zgliczyński,
    Rigorous Numerics for Dissipative PDEs III. An effective algorithm for rigorous integration of dissipative PDEs
    TMNA, 197-262 (2010)
  • P. Zgliczynski,
    Covering relations, cone conditions and stable manifold theorem
    Journal of Differential Equations, 1774--1819 (2009)
  • T. Kapela, P. Zgliczyński,
    A Lohner-type algorithm for control systems and ordinary differential inclusions
    Discrete Cont. Dyn. Sys. B 11, 365-385 (2009)
  • D. Wilczak, P. Zgliczyński,
    Period doubling in the Rössler system - a computer assisted proof
    Foundations of Computational Mathematics, 611--649 (2009)
  • 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, 1632--1663 (2009)
  • Ming Chia-Li, P. Zgliczyński,
    On stability of forcing relations for multidimensional perturbations of interval maps
    Fundamenta Mathematicae, 241--251 (2009)
  • Ming Chia-Li, Ming-Jiea Lyu, P. Zgliczyński,
    Topological entropy for multidimensional perturbations of snap-back repellers and one-dimensional maps
    Nonlinearity 21, 2555-2567 (2008)
  • H. Kokubu, D. Wilczak, P. Zgliczyński,
    Rigorous verification of cocoon bifurcations in the Michelson system
    Nonlinearity 20, 2147-2174 (2007)
  • M. Capiński, P. Zgliczyński,
    Covering Relations and Non-autonomous Perturbations of ODEs
    Discrete Cont. Dyn. Sys. A 14, 281-293 (2007)
  • 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, 629-652 (2007)
  • Z. Galias, P. Zgliczyński,
    An interval method for finding fixed points and periodic orbits of infinite dimensional discrete dynamical systems
    Int. J. of Bifurcation and Chaos 17, 4261-4272 (2007)
  • D. Wilczak, P. Zgliczyński,
    Heteroclinic Connections between Periodic Orbits in Planar Circular Restricted Three Body Problem - part II
    Communications in Mathematical Physics, Vol. 259, 561-576 (2006)
  • M. Gidea, P. Zgliczyński,
    Covering relations for multidimensional dynamical systems II
    Journal of Differential Equations 202/1, 59-80 (2005)
  • K. Wójcik, P. Zgliczyński,
    Topological horseshoes and delay differential equations
    Discrete Cont. Dyn. Sys. A 12, 827-852 (2005)
  • Roman Srzednicki, Klaudiusz Wójcik, Piotr Zgliczyński,
    Fixed point results based on the Ważewski method
    , (2005)
  • M. Gidea, P. Zgliczyński,
    Covering relations for multidimensional dynamical systems I
    Journal of Differential Equations 202/1, 32-58 (2004)
  • 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 (2004)
  • P. Zgliczyński,
    Rigorous numerics for dissipative Partial Differential Equations II. Periodic orbit for the Kuramoto-Sivashinsky PDE - a computer assisted proof
    Foundations of Computational Mathematics, 4, 157-185 (2004)
  • 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)
  • P. Zgliczyński,
    Attracting fixed points for the Kuramoto-Sivashinsky equation - a computer assisted proof
    SIAM Journal on Applied Dynamical Systems, Vol. 1, 215-235 (2003)
  • 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, 37-75 (2003)
  • Gianni Arioli, Piotr Zgliczyński,
    Periodic, homoclinic and heteroclinic orbits for H\'{e}non Heiles Hamiltonian near the critical energy level
    NONLINEARITY, 1833-1852 (2003)
  • T. Kapela, P. Zgliczyński,
    The existence of simple choreographies for the N-body problem - a computer assisted proof
    Nonlinearity, vol. 16, 1899-1918 (2003)
  • Piotr Zgliczyński,
    On smooth dependence on intial conditions for dissipative PDEs, an ODE-type approach
    J DIFFER EQUATIONS, 271-283 (2003)
  • Z. Galias, P. Zgliczyński,
    Abundance of homoclinic and heteroclinic orbits and rigorous bounds for the topological entropy for the Henon map
    Nonlinearity, 14, 909-932 (2002)
  • K. Wójcik, P. Zgliczyński,
    Isolating segments, fixed point index and symbolic dynamics III. Applications
    J. Diff. Eq. Vol. 183, 262-278 (2002)
  • P. Zgliczyński,
    C^1-Lohner algorithm
    Foundations of Computational Mathematics, 2, 429-465 (2002)
  • Piotr Zgliczyński,
    Attracting fixed points for the Kuramoto-Sivashinsky equation
    SIAM J APPL DYN SYST, 215-235 (2002)
  • G. Arioli, P. Zgliczyński,
    Symbolic dynamics for the Henon--Heiles hamiltonian on the critical energy level
    J. Diff. Eq. 171, 173-202 (2001)
  • P. Zgliczyński,
    On periodic points for systems of weakly coupled 1-dim maps
    Nonlinear Analysis. TMA, Vol 46/7, 1039-1062 (2001)
  • M. Mrozek, P. Zgliczyński,
    Set arithmetic and the enclosing problem in dynamics
    Annales Pol. Math., LXXIV, 237-259 (2001)
  • K. Wójcik, P. Zgliczyński,
    Isolating segments, fixed point index and symbolic dynamics II. Homoclinic solutions
    J. Diff. Eq. 172, 189-211 (2001)
  • M. Misiurewicz, P. Zgliczyński,
    Topological entropy for multidimensional perturbations of one dimensional maps
    Int. J. of Bifurcation and Chaos, vol. 11, 1443-1446 (2001)
  • K. Mischaikow, P. Zgliczyński,
    Rigorous Numerics for Partial Differential Equations: the Kuramoto-Sivashinsky equation
    Foundations of Computational Mathematics, 1, 255-288 (2001)
  • K. Wójcik, P. Zgliczyński,
    Isolating segments, fixed point index and symbolic dynamics
    J. Diff. Eq. 161, 245-288 (2000)
  • P. Zgliczyński,
    Symbolic dynamics for the R\"ossler folded towel map
    Conley Index Theory, Warsaw 1999, Banach Center Publications, Vol. 47, 253-258 (2000)
  • K. Wójcik, P. Zgliczyński,
    On existence of infinitely many homoclinic solutions
    Monatshefte fur Matematik 130, 155--160 (2000)
  • Klaudiusz Wójcik, Piotr Zgliczyński,
    How to show an existence of homoclinic trajectories using topological tools?
    , (2000)
  • Z. Galias, P. Zgliczyński,
    Computer assisted proof of chaos in the Lorenz system
    Physica D, 115, 165-188 (1999)
  • P. Zgliczyński,
    Multidimensional perturbations of one-dimensional maps and stability of Sharkovskii ordering
    Int. J. of Bifurcation and Chaos, Vol. 9, 1867-1876 (1999)
  • P. Zgliczyński,
    Sharkovskii's Theorem for multidimensional perturbations of one-dimensional maps
    Ergodic Theory and Dynamical Systems 19, 1655-1684 (1999)
  • P. Zgliczyński,
    Sharkovskii's Theorem for multidimensional perturbations of one-dimensional maps II
    Topological Methods in Nonlinear Analysis 14, 169-182 (1999)
  • P. Zgliczyński,
    Computer assisted proof of the horseshoe dynamics in the Henon map
    Random and Computational Dynamics, Vol. 5, 1-19 (1998)
  • A. Szymczak, K. Wójcik, P. Zgliczyński,
    On the discrete Conley index in the invariant subspace
    Topology and Applications, 87, 105-116 (1998)
  • 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 (1997)
  • P. Zgliczyński,
    Computer assisted proof of chaos in the Henon map and in the Rossler equations
    Nonlinearity 10, 243-252 (1997)
  • P. Zgliczyński,
    On dynamical System with an Integral Invariant on the Torus
    Univ. Iag. Acta Math. XXXII, 157-174 (1996)
  • 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)
  • P. Zgliczyński,
    Fixed point index for iterations, topological horseshoe and chaos
    Topological Methods in Nonlinear Analysis, Vol. 8, 169-177 (1996)
Division of Computational Mathematics, Institute of Computer Science, Łojasiewicza 6, 30-348 Kraków, Poland