E-mail address: umzglicz@cyf-kr.edu.pl

Preprints

Papers

Conference reports

- Calculus of Invariant Manifolds - topological approach
- Estimates of eigenspaces and eigenvalues of a matrix , joint work with Łukasz Struski and Jacek Tabor
- Real-number Computability from the Perspective of Computer Assisted Proofs in Analysis with Małgorzata Moczurad

- The number of relative equilibria in the PCR4PB with Jordi-Lluis Figueras and Warwick Tucker, Journal of Dynamics and Differential Equations
- Central configurations on the plane with $N$ heavy and $k$ light bodies with Małgorzata Moczurad, Communications in Nonlinear Science and Numerical Simulation, 114 (2022), 106533, https://doi.org/10.1016/j.cnsns.2022.106533
- Oscillatory Motions and Parabolic Manifolds at Infinity in the Planar Circular Restricted Three Body Problem with Maciej Capinski , Marcel Guardia, Tere Seara and Pau Martin Journal of Differential Equations, 320(2022) 316--370 https://doi.org/10.1016/j.jde.2022.02.056
- Recent advances in rigorous computation of Poincar\'e maps with Tomasz Kapela and Daniel Wilczak, Communications in Nonlinear Science and Numerical Simulation, 110 (2022) 106366, https://doi.org/10.1016/j.cnsns.2022.106366
- From the Sharkovskii theorem to periodic orbits for the Rossler system with Anna Gierzkiewicz, Journal of Differential Equations, 314(2022) 733-751, https://doi.org/10.1016/j.jde.2022.01.022
- Periodic orbits in Rossler system with Anna Gierzkiewicz, Communications in Nonlinear Science and Numerical Simulation, 101 (2021) 105891, https://doi.org/10.1016/j.cnsns.2021.105891
- Rigorous FEM for 1D Burgers equation with Piotr Kalita, SIAM Journal of Applied Dynamical Systems, (2021) 20(2), 853–907, https://doi.org/10.1137/20M1338216
- 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 - 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 101 (2021) 105578
- 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
- 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 - A computer-assisted proof of symbolic dynamics in Hyperion's rotation model with Anna Gierzkiewicz, program , Celestial Mechanics and Dynamical Astronomy (2019) 131:33
- 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
- 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
- Beyond the Melnikov method II: multidimensional setting with Maciej Capinski, Journal of Differential Equations, 265(2018) 3988–-4015
- 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
- Shadowing of non-transversal heteroclinic chains with Adria Simon and Amadeu Delshams, Journal of Differential Equations 264(2018), 3619–-3663
- 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
- Topological shadowing and the Grobman-Hartman Theorem, Topological Methods in Nonlinear Analysis, 50 (2017), 757--785
- Hyperbolicity and Averaging for the Srzednicki-Wójcik equation , Journal of Differential Equations , 262 (2017), 365-417
- On the Petras algorithm for verified integration of piecewise analytic functions , joint work with Małgorzata Moczurad, Journal of Complexity, 39 (2017), 69-93
- Beyond the Melnikov method: a computer assisted approach with Maciej Capinski, Journal of Differential Equations, 262 (2017), 365-417
- 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
- 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
- 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)
- 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
- 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
- Geometric proof for normally hyperbolic invariant manifolds with Maciej Capinski, Journal of Differential Equations, 259(2015) 6215--6286
- 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
- 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
- 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
- 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
- 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,
- Transition Tori in the Planar Restricted Elliptic Three Body Problem , with Maciej Capinski, Nonlinearity, 24 (2011) 1395-1432
*C*-Lohner algorithm, with D. Wilczak , Scheade Informaticae, Vol. 20, 9-46 (2011).^{n}- Cone Conditions and Covering Relations forNormally Hyperbolic Invariant Manifolds , with Maciej Capinski, Discrete and Continuous Dynamical Systems A, 30 (2011), 641-670
- 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
- On stability of forcing relations for multidimensional perturbationsof 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 ordinarydifferential inclusions, with Tomasz Kapela, Discrete and Continuous Dynamical Systems B, 11 (2009), 365-385
- 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
- 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 periodicorbits of infinite dimensional discrete dynamical systems, with Z. Galias, Int. J. of Bifurcation and Chaos 17, 4261--4272 (2007)
- Topological method for symmetric periodic orbitsfor maps with an reversing symmetry, with D. Wilczak, Discrete and Continuous Dynamical Systems A, 17, 629--652 (2007)
- Covering Relations and Non-autonomousPerturbations of ODEs , with Maciej Capinski,, Discrete and Continuous Dynamical Systems A, 14, 281--293 (2006)
- Heteroclinic Connections between Periodic Orbits inPlanar 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
- Covering relations for multidimensional dynamical systems I, with M. Gidea, J. of Diff. Equations, 202(2004) 32--58
- 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
- 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
- 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
- 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
- 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 inPlanar Restricted Circular Three Body Problem - A ComputerAssisted Proof , with D. Wilczak ,Comm. Math. Phys. 234 (2003) 1, 37-75,
*C*-Lohner algorithm , Foundations of Computational Mathematics, (2002) 2:429-465^{1}- 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 orbitsand rigorous bounds for the topological entropy for the Henon map, with Z. Galias, Nonlinearity, 14 (2001), 909-932
- Rigorous Numerics for Partial DifferentialEquations: 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 andsymbolic 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 ofone-dimensional maps II Topological Methods in Nonlinear Analysis (1999),14,169-182
- Sharkovskii's Theorem for multidimensional perturbations ofone-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 functionalboundary value problems for ODE's, Rivista di Matematica Pura e Applicata , 19, 1996 (101--105)
- Fixed point index for iterations, topological horseshoe andchaos, Topological Methods in Nonlinear Analysis, 1996, Vol. 8, No. 1, 169--177
- 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
- On dynamical System with an Integral Invariant on the Torus, Univ. Iag. Acta Math. , 1995, XXXII, 157--174

- 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
- Symbolic dynamics for the R\"ossler folded towel map,Conley Index Theory, Warszawa 1999, Banach Center Publulications Vol. 47,253--258
- Chaos in the Lorenz equations for classical parameter values.A computer assisted proof , with Z. Galias Univ. Iag. Acta Math. , 1998, XXXVI,
- 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