Piotr Zgliczynski

E-mail address: umzglicz@cyf-kr.edu.pl
Preprints
Papers
Conference reports

My Google Scholar

Preprints and papers pending

  1. Calculus of Invariant Manifolds - topological approach
  2. Estimates of eigenspaces and eigenvalues of a matrix , joint work with Łukasz Struski and Jacek Tabor
  3. Real-number Computability from the Perspective of Computer Assisted Proofs in Analysis with Małgorzata Moczurad
  4. Periodic orbits in Rossler system with Anna Gierzkiewicz

Papers

  1. Rigorous FEM for 1D Burgers equation with Piotr Kalita, SIAM Journal of Applied Dynamical Systems
  2. Central configurations in the spatial n-body problem for n=5,6 with equal masses with Małgorzata Moczurad, Celestial Mechanics and Dynamical Astronomy, (2020) 132:56, program with the instruction , binary files , report files: spatial-cc, planar-cc , Mathematica files with figures of spatial CC for 5 and 6 bodies
  3. CAPD: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems with Tomasz Kapela, Marian Mrozek and Daniel Wilczak, Communications in Nonlinear Science and Numerical Simulation
  4. A geometric method for infinite-dimensional chaos: Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line , a file with numerical data supplement.tgz, with Daniel Wilczak, Journal of Differential Equations, 269(2020) 8509--8548
  5. Central configurations in planar n-body problem for n=5,6,7 with equal masses with Małgorzata Moczurad program with the instruction , Celestial Mechanics and Dynamical Astronomy (2019) 131:46
  6. A computer-assisted proof of symbolic dynamics in Hyperion's rotation model with Anna Gierzkiewicz, program , Celestial Mechanics and Dynamical Astronomy (2019) 131:33
  7. On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditions with Piotr Kalita, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 150(2020) 2025--2054
  8. Computer assisted proof of the existence of the Lorenz attractor in the Shimizu-Morioka system with Maciej Capinski and Dimitry Turaev , Nonlinearity 31 (2018) 5410--5440
  9. Beyond the Melnikov method II: multidimensional setting with Maciej Capinski, Journal of Differential Equations, 265(2018) 3988–-4015
  10. Stabilizing the Long-time Behavior of the Navier-Stokes Equations and Damped Euler Systems by Large Mean Flow with Jacek Cyranka , Piotr B. Mucha and Edriss S. Titi, Physica D 369 (2018) 18–-29
  11. Shadowing of non-transversal heteroclinic chains with Adria Simon and Amadeu Delshams, Journal of Differential Equations 264(2018), 3619–-3663
  12. Algorithm for rigorous integration of Delay Differential Equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation with Robert Szczelina, Foundations of Computational Mathematics (2018) 18:1299--1332
  13. Topological shadowing and the Grobman-Hartman Theorem, Topological Methods in Nonlinear Analysis, 50 (2017), 757--785
  14. Hyperbolicity and Averaging for the Srzednicki-Wójcik equation , Journal of Differential Equations , 262 (2017), 365-417
  15. On the Petras algorithm for verified integration of piecewise analytic functions , joint work with Małgorzata Moczurad, Journal of Complexity, 39 (2017), 69-93
  16. Beyond the Melnikov method: a computer assisted approach with Maciej Capinski, Journal of Differential Equations, 262 (2017), 365-417
  17. Stabilizing effect of large average initial velocity in forced dissipative PDEs invariant with respect to Galilean transformations with Jacek Cyranka , Journal of Differential Equations, 261(2016) 4648-4708
  18. Existence of Periodic Solutions of the FitzHugh-Nagumo Equations for An Explicit Range of the Small Parameter, with Aleksander Czechowski, SIAM Journal of Applied Dynamical Systems, 15(2016), 1615–1655
  19. Connecting orbits for a singular nonautonomous real Ginzburg-Landau type equation with Daniel Wilczak, SIAM Journal of Applied Dynamical Systems, Vol. 15 No. (1), 495-525 (2016)
  20. New lower bound estimates for quadratures of bounded analytic functions , joint work with Małgorzata Moczurad and Włodzimierz Zwonek, Journal of Complexity, 34 (2016) 50-–67
  21. Quasi-decidability of a Fragment of the Analytic First-order Theory of Real Numbers , with Peter Franek and Stefan Ratschan , Journal of Automated Reasoning, 57 (2016) 157-–185
  22. Geometric proof for normally hyperbolic invariant manifolds with Maciej Capinski, Journal of Differential Equations, 259(2015) 6215--6286
  23. Rigorous numerics for PDEs with indefinite tail: existence of a periodic solution of the Boussinesq equation with time-dependent forcing , with Aleksander Czechowski, Schedae Informaticae, 24 (2015), 143--158
  24. Existence of globally attracting solutions for one-dimensional viscous Burgers equation with nonautonomous forcing - a computer assisted proof , with Jacek Cyranka , SIAM Journal of Applied Dynamical Systems, 14(2015) 787--821
  25. A homoclinic orbit in a planar singular ODE- a computer assisted proof. , with R. Szczelina , SIAM Journal of Applied Dynamical Systems 12 (2013), 1541-–1565
  26. Steady states bifurcations for theKuramoto-Sivashinsky equation - a computer assisted proof , a file with numerical data bifdata.txt , Journal of Computational Dynamics, 2 (2015), 95--142
  27. Satisfiability of Systems of Equations of Real Analytic Functions is Quasi-decidable , with Peter Franek and Stefan Ratschan Mathematical Foundations of Computer Science 2011, Lecture Notes in Computer Science 6907 (2011) 315-326,
  28. Transition Tori in the Planar Restricted Elliptic Three Body Problem , with Maciej Capinski, Nonlinearity, 24 (2011) 1395-1432
  29. Cn-Lohner algorithm, with D. Wilczak , Scheade Informaticae, Vol. 20, 9-46 (2011).
  30. Cone Conditions and Covering Relations forNormally Hyperbolic Invariant Manifolds , with Maciej Capinski, Discrete and Continuous Dynamical Systems A, 30 (2011), 641-670
  31. Rigorous Numerics for Dissipative PDEs III. An effectivealgorithm for rigorous integration of dissipativePDEs, a file with numerical data proofs.zip, the program and installation instruction, Topological Methods in Nonlinear Analysis, 36 (2010) 197–262
  32. On stability of forcing relations for multidimensional perturbationsof interval maps with Ming-Chia Li, Fund. Math. 206 (2009) 241-251
  33. 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)
  34. Covering relations, cone conditions and stable manifold theorem, J. of Diff. Equations 246 (2009) 1774--1819
  35. Period doubling in the R\"ossler system - a computer assisted proof, with D. Wilczak, Foundations of Computational Mathematics, 9 (2009) 611-649
  36. A Lohner-type algorithm for control systems and ordinarydifferential inclusions, with Tomasz Kapela, Discrete and Continuous Dynamical Systems B, 11 (2009), 365-385
  37. Topological entropy for multidimensional perturbations of snap-backrepellers and one-dimensional maps, with Ming-Chia Li and Ming-Jiea Lyu, Nonlinearity 21 (2008) 2555-2567
  38. Rigorous verification of cocoon bifurcations in the Michelson system with H. Kokubu and D. Wilczak, Nonlinearity 20 (2007) 2147-2174
  39. An interval method for finding fixed points and periodicorbits of infinite dimensional discrete dynamical systems, with Z. Galias, Int. J. of Bifurcation and Chaos 17, 4261--4272 (2007)
  40. Topological method for symmetric periodic orbitsfor maps with an reversing symmetry, with D. Wilczak, Discrete and Continuous Dynamical Systems A, 17, 629--652 (2007)
  41. Covering Relations and Non-autonomousPerturbations of ODEs , with Maciej Capinski,, Discrete and Continuous Dynamical Systems A, 14, 281--293 (2006)
  42. Heteroclinic Connections between Periodic Orbits inPlanar Restricted Circular Three Body Problem - Part II, with D. Wilczak, Comm. Math. Phys. 259, 561-576 (2005),
  43. 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,
  44. Topological horseshoes and delay differential equations, with K. Wojcik, Discrete and Continuous Dynamical Systems A, 12 (2005), 827--852
  45. Covering relations for multidimensional dynamical systems II, with M. Gidea, J. of Diff. Equations 202(2004) 59--80
  46. Covering relations for multidimensional dynamical systems I, with M. Gidea, J. of Diff. Equations, 202(2004) 32--58
  47. Rigorous numerics for dissipative PartialDifferential Equations II.Periodic orbit for the Kuramoto-Sivashinsky PDE - a computerassisted proof, Foundations of Computational Mathematics, 4 (2004), 157--185
  48. On smooth dependence on intial conditions for dissipative PDEs, an ODE-type approach, J. of Diff. Equations, 195/2 (2003), 271--283
  49. 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
  50. Periodic, homoclinic and heteroclinic orbits for Henon Heiles Hamiltonian near the critical energy level, with Gianni Arioli, Nonlinearity, vol. 16, No. 5 (2003), 1833--1852
  51. Trapping regions and ODE-type proof ofan existence and uniqueness for Navier-Stokes equations with periodic boundaryconditions on the plane, Univ. Iag. Acta Math. 41(2003) 89-113
  52. Attracting fixed points for the Kuramoto-Sivashinsky equation , SIAM Journal on Applied Dynamical Systems,(2002) Volume 1, Number 2 pp. 215-235
  53. Heteroclinic Connections between Periodic Orbits inPlanar Restricted Circular Three Body Problem - A ComputerAssisted Proof , with D. Wilczak ,Comm. Math. Phys. 234 (2003) 1, 37-75,
  54. C1-Lohner algorithm , Foundations of Computational Mathematics, (2002) 2:429-465
  55. Isolating segments, fixed point index and symbolic dynamics III. Applications. with K. Wojcik J. Diff. Eq. Vol. 183, No. 1, (2002), pp. 262-278
  56. Abundance of homoclinic and heteroclinic orbitsand rigorous bounds for the topological entropy for the Henon map, with Z. Galias, Nonlinearity, 14 (2001), 909-932
  57. Rigorous Numerics for Partial DifferentialEquations: the Kuramoto-Sivashinsky equation., with K. Mischaikow, Foundations of Computational Mathematics, (2001) 1:255-288
  58. 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
  59. Isolating segments, fixed point index andsymbolic dynamics II. Homoclinic solutions. , with K. Wojcik, J. of Diff. Equations, 172, 189--211 (2001)
  60. Symbolic dynamics for the H\'enon--Heiles hamiltonian on the critical energy level , with Gianni Arioli, Journal of Diff. Equations, 171, 173-202 (2001)
  61. On periodic points for systems of weakly coupled 1-dim maps,Nonlinear Analysis TMA, Vol 46/7, 1039-1062 (2001)
  62. Set arithmetics and the enclosing problem in dynamics , with Marian Mrozek , Ann. Pol. Mat. (2000), 237--259
  63. On existence of infinitely many homoclinic solutions. with K. Wojcik , Monatshetfe fur Mathematik, 130, 155-160 (2000)
  64. Isolating segments, fixed point index and symbolic dynamics with K. Wojcik, Journal of Diff. Equations, 161, 245--288, (2000)
  65. Multidimensional perturbations of one-dimensional maps and stability of Sharkovskii ordering, Int. J. of Bifurcations and Chaos, Vol. 9, No. 9, (1999), 1867-1876
  66. Sharkovskii's Theorem for multidimensional perturbations ofone-dimensional maps II Topological Methods in Nonlinear Analysis (1999),14,169-182
  67. Sharkovskii's Theorem for multidimensional perturbations ofone-dimensional maps, Erg. Th. & Dyn. Systems, (1999), 19, 1655--1684
  68. Computer assisted proof of chaos in the Lorenz system, Z. Galias Physica D, 115(1998), 165-188
  69. On the discrete Conley index in the invariant subspace, with K. Wojcik and A. Szymczak, Topology and Applications, 87(1998) ,105-116,
  70. Computer assisted proof of the horseshoe dynamics in the H\'enon map, Random \& Computational Dynamics, Vol. 5, No.1, 1997, 1--19
  71. Computer assisted proof of chaos in the H\'enon map and in the R\"ossler equations, Nonlinearity, 1997, Vol. 10, No. 1, 243--252
  72. An existence theorem for perturbation of nonlinear functionalboundary value problems for ODE's, Rivista di Matematica Pura e Applicata , 19, 1996 (101--105)
  73. Fixed point index for iterations, topological horseshoe andchaos, Topological Methods in Nonlinear Analysis, 1996, Vol. 8, No. 1, 169--177
  74. On a Matched Pair of Lie Groups for the $\kappa$-Poincar\'e in2-Dimensions, with A. Sitarz, Mathematical Physics Electronic Journal 1996, Vol. 2, No. 5, pp. 8
  75. On dynamical System with an Integral Invariant on the Torus, Univ. Iag. Acta Math. , 1995, XXXII, 157--174

Conference reports

  1. How to show an existence of homoclinic trajectories using topological tools ? , with K. Wojcik , Equadiff'99 , 246-248, Editors: B. Fiedler, K. Gr\"oger, J. Sprekels. 2000, World Scientific, Singapore, New Jersey, London, Hong-Kong
  2. Symbolic dynamics for the R\"ossler folded towel map,Conley Index Theory, Warszawa 1999, Banach Center Publulications Vol. 47,253--258
  3. Chaos in the Lorenz equations for classical parameter values.A computer assisted proof , with Z. Galias Univ. Iag. Acta Math. , 1998, XXXVI,
  4. Rigorous verification of chaos in the R\"ossler equations, Scientific Computing and Validated Numerics, G. Alefeld, A. Frommer and B. Lang editors, Akademie Verlag, Berlin, 1996, 287--292