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prof. dr hab. Piotr Zgliczyński
Zakład Matematyki Komputerowej profesor zwyczajny
Kontakt:
  • tel. +48 18 44 99 250
  • e-mail: pzgliczynski@wsb-nlu.edu.pl
  • pokój: C230

Biografia:

- 2007, profesor in mathematics
- 2002, habilitation in mathematics at Jagiellonian University
- 1996, Ph. D. in mathematics at Jagiellonian University
- 1990, M. of Sc. in theoretical physics at Jagiellonian University
- 1988, M. of Sc. in mathematics at Jagiellonian University

Obszar zainteresowań:

- dynamical systems, ordinary and partial di®erential equations
- chaos theory
- rigorous numerical methods for ODE's and PDE's
- computer assisted proofs in dynamical systems

Publikacje:

  • Transition Tori in the Planar Restricted Elliptic Three Body Problem , with Maciej Capinski , Nonlinearity, 24 (2011) 1395-1432
  • C^n-Lohner algorithm , with D. Wilczak , Scheade Informaticae, Vol. 20, 9-46 (2011).
  • Cone Conditions and Covering Relations for Normally Hyperbolic Invariant Manifolds , with Maciej Capinski , Discrete and Continuous Dynamical Systems A , 30 (2011), 641-670
  • Rigorous Numerics for Dissipative PDEs III. An effective algorithm for rigorous integration of dissipative PDEs, a file with numerical data proofs.zip , the program and installation instruction , Topological Methods in Nonlinear Analysis, 36 (2010) 197-262
  • On stability of forcing relations for multidimensional perturbations of interval maps with Ming-Chia Li , Fund. Math. 206 (2009) 241-251
  • Computer assisted proof of the existence of homoclinic tangency for the Henon map and for the forced-damped pendulum , with D. Wilczak , SIAM Journal of Applied Dynamical Systems 8, Issue 4, pp. 1632-1663 (2009)
  • Covering relations, cone conditions and stable manifold theorem , J. of Diff. Equations 246 (2009) 1774-1819
  • Period doubling in the R\"ossler system - a computer assisted proof , with D. Wilczak , Foundations of Computational Mathematics, 9 (2009) 611-649
  • A Lohner-type algorithm for control systems and ordinary differential inclusions , with Tomasz Kapela , Discrete and Continuous Dynamical Systems B, 11 (2009), 365-385
  • Topological entropy for multidimensional perturbations of snap-back repellers and one-dimensional maps , with Ming-Chia Li and Ming-Jiea Lyu , Nonlinearity 21 (2008) 2555-2567
  • Rigorous verification of cocoon bifurcations in the Michelson system with H. Kokubu and D. Wilczak , Nonlinearity 20 (2007) 2147-2174
  • An interval method for finding fixed points and periodic orbits of infinite dimensional discrete dynamical systems, with Z. Galias , Int. J. of Bifurcation and Chaos 17, 4261--4272 (2007)
  • Topological method for symmetric periodic orbits for maps with an reversing symmetry , with D. Wilczak , Discrete and Continuous Dynamical Systems A, 17, 629-652 (2007)
  • Covering Relations and Non-autonomous Perturbations of ODEs , with Maciej Capinski, Discrete and Continuous Dynamical Systems A, 14, 281--293 (2006)
  • Heteroclinic Connections between Periodic Orbits in Planar Restricted Circular Three Body Problem - Part II , with D. Wilczak , Comm. Math. Phys. 259, 561-576 (2005),
  • Fixed point results based on the Wazewski method , with R. Srzednicki and K. Wojcik , in "Handbook of topological fixed point theory", Edited by: R.Brown, M. Furi, L. Górniewicz and B. Jiang , 903- 941, Kluwer 2004,
  • Topological horseshoes and delay differential equations , with K. Wojcik, Discrete and Continuous Dynamical Systems A, 12 (2005), 827--852
  • Covering relations for multidimensional dynamical systems II, with M. Gidea , J. of Diff. Equations 202(2004) 59--80
  • Rigorous numerics for dissipative Partial Differential Equations II. Periodic orbit for the Kuramoto-Sivashinsky PDE - a computer assisted proof , Foundations of Computational Mathematics, 4 (2004), 157--185
  • On smooth dependence on intial conditions for dissipative PDEs, an ODE-type approach , J. of Diff. Equations, 195/2 (2003), 271--283
  • The existence of simple choreographies for N-body problem - a computer assisted proof , with Tomasz Kapela , a C++-program used in this paper can be downloaded here , Nonlinearity, vol. 16 (2003), 1899-1918
  • The existence of simple choreographies for N-body problem - a computer assisted proof , with Tomasz Kapela , a C++-program used in this paper can be downloaded here , Nonlinearity, vol. 16 (2003), 1899-1918
  • Trapping regions and ODE-type proof of an existence and uniqueness for Navier-Stokes equations with periodic boundary conditions on the plane, Univ. Iag. Acta Math. 41 (2003) 89-113
  • Attracting fixed points for the Kuramoto-Sivashinsky equation , SIAM Journal on Applied Dynamical Systems,(2002) Volume 1, Number 2 pp. 215-235
  • Heteroclinic Connections between Periodic Orbits in Planar Restricted Circular Three Body Problem - A Computer Assisted Proof , with D. Wilczak , Comm. Math. Phys. 234 (2003) 1, 37-75,
  • C^1-Lohner algorithm , Foundations of Computational Mathematics, (2002) 2:429-465
  • Isolating segments, fixed point index and symbolic dynamics III. Applications. with K. Wojcik J. Diff. Eq. Vol. 183, No. 1, (2002), pp. 262-278
  • Abundance of homoclinic and heteroclinic orbits and rigorous bounds for the topological entropy for the Henon map, with Z. Galias , Nonlinearity, 14 (2001), 909-932
  • Rigorous Numerics for Partial Differential Equations: the Kuramoto-Sivashinsky equation., with K. Mischaikow , Foundations of Computational Mathematics, (2001) 1:255-288
  • Topological entropy for multidimensional perturbations of one dimensional maps, with M. Misiurewicz Int. J. of Bifurcation and Chaos, Vo. 11, No.5 (2001), 1443-1446
  • Isolating segments, fixed point index and symbolic dynamics II. Homoclinic solutions. , with K. Wojcik, J. of Diff. Equations, 172, 189--211 (2001)
  • Symbolic dynamics for the H\'enon--Heiles hamiltonian on the critical energy level , with Gianni Arioli, Journal of Diff. Equations, 171, 173-202 (2001)
  • On periodic points for systems of weakly coupled 1-dim maps, Nonlinear Analysis TMA, Vol 46/7, 1039-1062 (2001)
  • Set arithmetics and the enclosing problem in dynamics , with Marian Mrozek , Ann. Pol. Mat. (2000), 237--259
  • On existence of infinitely many homoclinic solutions. with K. Wojcik , Monatshetfe fur Mathematik, 130, 155-160 (2000)
  • Isolating segments, fixed point index and symbolic dynamics with K. Wojcik, Journal of Diff. Equations, 161, 245--288, (2000)
  • Multidimensional perturbations of one-dimensional maps and stability of Sharkovskii ordering, Int. J. of Bifurcations and Chaos, Vol. 9, No. 9, (1999), 1867-1876
  • Sharkovskii's Theorem for multidimensional perturbations of one-dimensional maps II Topological Methods in Nonlinear Analysis (1999),14,169-182
  • Sharkovskii's Theorem for multidimensional perturbations of one-dimensional maps, Erg. Th. & Dyn. Systems, (1999), 19, 1655--1684
  • Computer assisted proof of chaos in the Lorenz system, Z. Galias Physica D, 115(1998), 165-188
  • On the discrete Conley index in the invariant subspace, with K. Wojcik and A. Szymczak, Topology and Applications, 87(1998) ,105-116,
  • Computer assisted proof of the horseshoe dynamics in the H\'enon map, Random \& Computational Dynamics, Vol. 5, No.1, 1997, 1--19
  • Computer assisted proof of chaos in the H\'enon map and in the R\"ossler equations, Nonlinearity, 1997, Vol. 10, No. 1, 243--252
  • An existence theorem for perturbation of nonlinear functional boundary value problems for ODE's, Rivista di Matematica Pura e Applicata , 19, 1996 (101--105)
  • Fixed point index for iterations, topological horseshoe and chaos, Topological Methods in Nonlinear Analysis, 1996, Vol. 8, No. 1, 169--177
  • On a Matched Pair of Lie Groups for the $\kappa$-Poincar\'e in 2-Dimensions, with A. Sitarz, Mathematical Physics Electronic Journal 1996, Vol. 2, No. 5, pp. 8
  • On dynamical System with an Integral Invariant on the Torus, Univ. Iag. Acta Math. , 1995, XXXII, 157--174