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:
1988 | M.S. in matchematics | Jagiellonian University |
1990 | M.S. in theoretical physics | Jagiellonian University |
1996 | PhD in mathematics | Jagiellonian University |
2002 | habilitation in mathematics | Jagiellonian University |
2008 | profesor in mathematics | Jagiellonian University |
1998/1999 | NSF-NATO postdoc | Georgia Institute of Technology, Atlanta, USA |
1999/2000 | postdoc | Georgia Institute of Technology, Atlanta, USA |
2000/2001 | visiting profesor | Indiana University, Bloomington, USA |
Awards and scholarships:
1998 | NSF-NATO postdoctoral fellowship | NSF, USA |
2008 | Polish Prime Minister award for outstanding scientific achievement | polish goverment |
Research grants:
1998-2000 | Metody topologiczne w wielowymiarowych chaotycznych układach dynamicznych. Topologiczna hiperboliczność | KBN, Poland |
2002-2005 | Dynamika 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:
- Jakub Banaśkiewicz, Piotr Kalita, Piotr Zgliczyński,Computer-assisted validation of the existence of periodic orbit in the Brusselator systemAdvances in Differential Equations, vol. 29, 815-862 (2024)
- 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 DelaysFOUNDATIONS OF COMPUTATIONAL MATHEMATICS, vol. 24, 1389-1454 (2024)
- Anna Gierzkiewicz-Pieniążek, Piotr Zgliczyński,From the Sharkovskii theorem to periodic orbits for the R\"ossler systemJOURNAL OF DIFFERENTIAL EQUATIONS, vol. 314, 733-751 (2022)
- Maciej Capiński, Marcel Guardia, Pau Martin , Tere Seara, Piotr Zgliczyński,Oscillatory Motions and Parabolic Manifolds at Infinity in the Planar Circular Restricted Three Body ProblemJOURNAL OF DIFFERENTIAL EQUATIONS, vol. 320, 316-370 (2022)
- Tomasz Kapela, Daniel Wilczak, Piotr Zgliczyński,Recent advances in a rigorous computation of Poincaré mapsCommunications in Nonlinear Science and Numerical Simulation, vol. 110, 106366 (2022)
- Piotr Zgliczyński, Małgorzata Moczurad,Central configurations on the plane with N heavy and k light bodiesCommunications in Nonlinear Science and Numerical Simulation, vol. 114, 4991-4998 (2022)
- Tomasz Kapela, Marian Mrozek, Daniel Wilczak, Piotr Zgliczyński,CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systemsCommunications in Nonlinear Science and Numerical Simulation, vol. 101, 105578 (2021)
- Piotr Kalita, Piotr Zgliczyński,Rigorous FEM for 1D Burgers EquationSIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 20, 853–907 (2021)
- Anna Gierzkiewicz-Pieniążek, Piotr Zgliczyński,Periodic orbits in R\"ossler systemCommunications in Nonlinear Science and Numerical Simulation, vol. 101, 105891 (2021)
- Piotr Kalita, Piotr Zgliczyński,On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditionsPROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION AMATHEMATICS, vol. 150, 2025-2054 (2020)
- Daniel Wilczak, Piotr Zgliczyński,A geometric method for infinite-dimensional chaos: Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the lineJOURNAL OF DIFFERENTIAL EQUATIONS, vol. 269, 8509-8548 (2020)
- Małgorzata Moczurad, Piotr Zgliczyński,Central configurations in spatial $n$-body problem for $n=5,6$ with equal massesCELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 132:56 (2020)
- Anna Gierzkiewicz-Pieniążek, Piotr Zgliczyński,A computer-assisted proof of symbolic dynamics in Hyperion's rotation modelCELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, vol. 131, 33 (2019)
- Małgorzata Moczurad, Piotr Zgliczyński,Central configurations in planar $n$-body problem for $n=5,6,7$ with equal massesCELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, vol. 131, 46 (2019)
- Amadeu Delshams, Adria Simon, Piotr Zgliczyński,Shadowing of non-transversal heteroclinic chainsJOURNAL OF DIFFERENTIAL EQUATIONS, vol. 264, 3619–-3663 (2018)
- Robert Szczelina, Piotr Zgliczyński,Algorithm for rigorous integration of Delay Differential Equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equationFOUNDATIONS OF COMPUTATIONAL MATHEMATICS, vol. 18, 1299-1332 (2018)
- 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 flowPHYSICA D-NONLINEAR PHENOMENA, vol. 369, 18-29 (2018)
- Maciej Capiński, Dmitry Turaev, Piotr Zgliczyński,Computer assisted proof of the existence of the Lorenz attractor in the Shimizu–Morioka systemNONLINEARITY, vol. 31, 5410 (2018)
- Maciej Capiński, Piotr Zgliczyński,Beyond the Melnikov method II: Multidimensional settingJOURNAL OF DIFFERENTIAL EQUATIONS, vol. 265, 3988-4015 (2018)
- Piotr Zgliczyński,Hyperbolicity and Averaging for the Srzednicki-W{'o}jcik equationJOURNAL OF DIFFERENTIAL EQUATIONS, vol. 262, 1931-1955 (2017)
- Maciej Capiński, Piotr Zgliczyński,Beyond the Melnikov method: a computer assisted approachJOURNAL OF DIFFERENTIAL EQUATIONS, vol. 262, 365-417 (2017)
- Piotr Zgliczyński,Topological shadowing and the Grobman-Hartman TheoremTopological Methods in Nonlinear Analysis, vol. 50, 757-785 (2017)
- Małgorzata Moczurad, Piotr Zgliczyński,On the Petras algorithm for verified integration of piecewise analytic functionsJOURNAL OF COMPLEXITY, vol. 39 , 69-93 (2017)
- Małgorzata Moczurad, Piotr Zgliczyński, Włodzimierz Zwonek,New lower bound estimates for quadratures of bounded analytic functionsJOURNAL OF COMPLEXITY, vol. 34, 50–67 (2016)
- Aleksander Czechowski, Piotr Zgliczyński,Existence of periodic solutions of the FitzHugh-Nagumo equations for an explicit range of the small parameterSIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 15(3), 1615-1655 (2016)
- Stefan Ratschan , Peter Franek, Piotr Zgliczyński,Quasi-decidability of a Fragment of the Analytic First-order Theory of Real NumbersJOURNAL OF AUTOMATED REASONING, vol. 57, 157-185 (2016)
- Daniel Wilczak, Piotr Zgliczyński,Connecting Orbits for a Singular Nonautonomous Real Ginzburg--Landau Type EquationSIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 15, 495-525 (2016)
- Jacek Cyranka, Piotr Zgliczyński,Stabilizing effect of large average initial velocity in forced dissipative PDEs invariant with respect to Galilean transformationsJOURNAL OF DIFFERENTIAL EQUATIONS, vol. 261, 4648-4708 (2016)
- Jacek Cyranka, Piotr Zgliczyński,Existence of globally attracting solutions for one-dimensional viscous Burgers equation with nonautonomous forcing - a computer assisted proofSIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 14, 787-821 (2015)
- Maciej Capiński, Piotr Zgliczyński,Geometric proof for normally hyperbolic invariant manifoldsJOURNAL OF DIFFERENTIAL EQUATIONS, vol. 259, 6215-6286 (2015)
- Piotr Zgliczyński,Steady states bifurcations for the Kuramoto-Sivashinsky equation - a computer assisted proofJournal of Computational Dynamics AIMS, 95-142 (2015)
- Aleksander Czechowski, Piotr Zgliczyński,Rigorous numerics for PDEs with indefinite tail: existence of a periodic solution of the Boussinesq equation with time-dependent forcingSchedae Informaticae, vol. 24, 143-158 (2015)
- M. Capiński, P. Zgliczyński,Geometric proof for normally hyperbolic invariant manifoldsJ. Diff. Eq., 259, 6215--6286 (2015)
- Robert Szczelina, Piotr Zgliczyński,A Homoclinic Orbit in a Planar Singular ODE---A Computer Assisted ProofSIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 12, 1541-–1565 (2013)
- Maciej Capiński, Piotr Zgliczyński,Cone Conditions and Covering Relations for Normally Hyperbolic Invariant ManifoldsDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, vol. 30, 641-670 (2011)
- Daniel Wilczak, Piotr Zgliczyński,C^r-Lohner algorithmSchedae Informaticae, vol. 20, 9-46 (2011)
- Stefan Ratschan , Peter Franek, Piotr Zgliczyński,Satisfiability of Systems of Equations of Real Analytic Functions is Quasi-decidableLECTURE NOTES IN COMPUTER SCIENCE, vol. 6907, 315-326 (2011)
- Maciej Capiński, Piotr Zgliczyński,Transition Tori in the Planar Restricted Elliptic Three Body ProblemNONLINEARITY, vol. 24, 1395-1432 (2011)
- Piotr Zgliczyński,Rigorous Numerics for Dissipative PDEs III. An effective algorithm for rigorous integration of dissipative PDEsTopological Methods in Nonlinear Analysis, vol. 36, 197-262 (2010)
- Li Ming-Chia, Piotr Zgliczyński,On stability of forcing relations for multidimensional perturbations of interval mapsFUNDAMENTA MATHEMATICAE, vol. 206, 241-251 (2009)
- Daniel Wilczak, Piotr Zgliczyński,Computer assisted proof of the existence of homoclinic tangency for the Henon map and for the forced-damped pendulumSIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 8, 1632-1663 (2009)
- Daniel Wilczak, Piotr Zgliczyński,Period doubling in the Rössler system - a computer assisted proofFOUNDATIONS OF COMPUTATIONAL MATHEMATICS, vol. 9, 611-649 (2009)
- Tomasz Kapela, Piotr Zgliczyński,A Lohner-type algorithm for control systems and ordinary differential inclusionsDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, vol. 11, 365-385 (2009)
- Piotr Zgliczyński,Covering relations, cone conditions and stable manifold theoremJOURNAL OF DIFFERENTIAL EQUATIONS, vol. 246, 1774-1819 (2009)
- Li Ming-Chia, Lyu Ming-Jiea , Piotr Zgliczyński,Topological entropy for multidimensional perturbations of snap-back repellers and one-dimensional mapsNONLINEARITY, vol. 21, 2555-2567 (2008)
- Daniel Wilczak, Piotr Zgliczyński,Topological method for symmetric periodic orbits for maps with a reversing symmetryDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, vol. 17, 629-652 (2007)
- Zbigniew Galias, Piotr Zgliczyński,An interval method for finding fixed points and periodic orbits of infinite dimensional discrete dynamical systemsINTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, vol. 17, 4261-4272 (2007)
- Hiroshi Kokubu, Daniel Wilczak, Piotr Zgliczyński,Rigorous verification of cocoon bifurcations in the Michelson systemNONLINEARITY, vol. 20, 2147-2174 (2007)
- Maciej Capiński, Piotr Zgliczyński,Covering Relations and Non-autonomous Perturbations of ODEsDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, vol. 14, 281-293 (2006)
- Klaudiusz Wójcik, Piotr Zgliczyński,Topological horseshoes and delay differential equationsDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, vol. 12, 827-852 (2005)
- Daniel Wilczak, Piotr Zgliczyński,Heteroclinic Connections between Periodic Orbits in Planar Circular Restricted Three Body Problem - part IICOMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 259, 561-576 (2005)
- Roman Srzednicki, Klaudiusz Wójcik, Piotr Zgliczyński,Fixed point results based on the Ważewski methodSpringer Verlag (połaczony z Kluwer Academic Publishing), 905-943 (2005)
- marian gidea, Piotr Zgliczyński,Covering relations for multidimensional dynamical systems IJOURNAL OF DIFFERENTIAL EQUATIONS, vol. 202, 32-58 (2004)
- marian gidea, Piotr Zgliczyński,Covering relations for multidimensional dynamical systems IIJOURNAL OF DIFFERENTIAL EQUATIONS, vol. 202, 59-80 (2004)
- Piotr Zgliczyński,Rigorous numerics for dissipative Partial Differential Equations II. Periodic orbit for the Kuramoto-Sivashinsky PDE - a computer assisted proofFOUNDATIONS OF COMPUTATIONAL MATHEMATICS, vol. 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 planeUniv. Iag. Acta Math. 41, 89-113 (2003)
- P. Zgliczyński,On smooth dependence on initial conditions for dissipative PDEs, an ODE-type approachJournal of Differential Equations 195/2 271-283, 271-283 (2003)
- Tomasz Kapela, Piotr Zgliczyński,The existence of simple choreographies for the N-body problem - a computer assisted proofNONLINEARITY, vol. 16(2), 1899-1918 (2003)
- Daniel Wilczak, Piotr Zgliczyński,Heteroclinic Connections between Periodic Orbits in Planar Circular Restricted Three Body Problem - A Computer Assisted ProofCOMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 234, 37-75 (2003)
- Piotr Zgliczyński,On smooth dependence on intial conditions for dissipative PDEs, an ODE-type approachJOURNAL OF DIFFERENTIAL EQUATIONS, vol. 195/2, 271-283 (2003)
- Gianni Arioli, Piotr Zgliczyński,Periodic, homoclinic and heteroclinic orbits for H'{e}non Heiles Hamiltonian near the critical energy levelNONLINEARITY, vol. vol. 16, No. 5, 1833-1852 (2003)
- Piotr Zgliczyński,C^1-Lohner algorithmFOUNDATIONS OF COMPUTATIONAL MATHEMATICS, vol. 2, 429-465 (2002)
- Klaudiusz Wójcik, Piotr Zgliczyński,Isolating segments, fixed point index, and symbolic dynamics. III. ApplicationsJOURNAL OF DIFFERENTIAL EQUATIONS, vol. 183, 262-278 (2002)
- Piotr Zgliczyński,Attracting fixed points for the Kuramoto-Sivashinsky equationSIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 1, 215-235 (2002)
- P. Zgliczyński,Attracting fixed points for the Kuramoto-Sivashinsky equation - a computer assisted proofSIAM Journal on Applied Dynamical Systems, Vol. 1, 215-235 (2002)
- P. Zgliczyński,On periodic points for systems of weakly coupled 1-dim mapsNonlinear Analysis. TMA, Vol 46/7, 1039-1062 (2001)
- G. Arioli, P. Zgliczyński,Symbolic dynamics for the Henon--Heiles hamiltonian on the critical energy levelJ. Diff. Eq. 171, 173-202 (2001)
- M. Misiurewicz, P. Zgliczyński,Topological entropy for multidimensional perturbations of one dimensional mapsInt. J. of Bifurcation and Chaos, vol. 11, 1443-1446 (2001)
- Klaudiusz Wójcik, Piotr Zgliczyński,Isolating segments, fixed point index, and symbolic dynamics. II. Homoclinic solutions.JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 172, 189-211 (2001)
- Konstantin Mischaikov, Piotr Zgliczyński,Rigorous Numerics for Partial Differential Equations: the Kuramoto-Sivashinsky equationFOUNDATIONS OF COMPUTATIONAL MATHEMATICS, vol. 1, 255-288 (2001)
- M. Mrozek, P. Zgliczyński,Set arithmetic and the enclosing problem in dynamicsAnnales Pol. Math., LXXIV, 237-259 (2000)
- Klaudiusz Wójcik, Piotr Zgliczyński,Isolating segments, fixed point index, and symbolic dynamicsJOURNAL OF DIFFERENTIAL EQUATIONS, vol. 161, 245-288 (2000)
- 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)
- Klaudiusz Wójcik, Piotr Zgliczyński,On existence of infinitely many homoclinic solutionsMONATSHEFTE FUR MATHEMATIK, vol. 130, 155-160 (2000)
- P. Zgliczyński,Multidimensional perturbations of one-dimensional maps and stability of Sharkovskii orderingInt. J. of Bifurcation and Chaos, Vol. 9, 1867-1876 (1999)
- P. Zgliczyński,Sharkovskii's Theorem for multidimensional perturbations of one-dimensional mapsErgodic Theory and Dynamical Systems 19, 1655-1684 (1999)
- P. Zgliczyński,Sharkovskii's Theorem for multidimensional perturbations of one-dimensional maps IITopological Methods in Nonlinear Analysis 14, 169-182 (1999)
- P. Zgliczyński,Symbolic dynamics for the R\"ossler folded towel mapConley Index Theory, Warsaw 1999, Banach Center Publications, Vol. 47, 253-258 (1999)
- Andrzej Szymczak , Klaudiusz Wójcik, Piotr Zgliczyński,On the discrete Conley index in the invariant subspaceTOPOLOGY AND ITS APPLICATIONS, vol. 87, 105-115 (1998)
- Z. Galias, P. Zgliczyński,Computer assisted proof of chaos in the Lorenz systemPhysica D, 115, 165-188 (1998)
- P. Zgliczyński,Computer assisted proof of chaos in the Henon map and in the Rossler equationsNonlinearity 10, 243-252 (1997)
- P. Zgliczyński,Computer assisted proof of the horseshoe dynamics in the Henon mapRandom and Computational Dynamics, Vol. 5, 1-19 (1997)
- A. Sitarz, P. Zgliczyński,On a Matched Pair of Lie Groups for the $\kappa$-Poincar\'e in 2-DimensionsMathematical Physics Electronic Journal, Vol. 2, pp. 8 (1996)
- P. Zgliczyński,Fixed point index for iterations, topological horseshoe and chaosTopological Methods in Nonlinear Analysis, Vol. 8, 169-177 (1996)
- P. Zgliczyński,An existence theorem for perturbation of nonlinear functional boundary value problems for ODE'sRivista di Matematica Pura e Applicata 19, 101-105 (1996)
- P. Zgliczyński,On dynamical System with an Integral Invariant on the TorusUniv. Iag. Acta Math. XXXII, 157-174 (1995)
- Piotr Zgliczyński,Abundance of homoclinic and heteroclinic orbits and rigorous bounds for the topological entropy for the Henon mapNONLINEARITY, vol. 14, 909-932 ()