Kalita, Piotr; Zgliczyński, Piotr Rigorous FEM for one-dimensional Burgers equation. (English) Zbl 1528.65072 SIAM J. Appl. Dyn. Syst. 20, No. 2, 853-907 (2021). MSC: 65M60 35B10 37L05 37M15 35Q53 68V15 PDFBibTeX XMLCite \textit{P. Kalita} and \textit{P. Zgliczyński}, SIAM J. Appl. Dyn. Syst. 20, No. 2, 853--907 (2021; Zbl 1528.65072) Full Text: DOI arXiv
Gierzkiewicz, Anna; Zgliczyński, Piotr Periodic orbits in the Rössler system. (English) Zbl 1472.34060 Commun. Nonlinear Sci. Numer. Simul. 101, Article ID 105891, 13 p. (2021). MSC: 34C05 34A34 34C28 PDFBibTeX XMLCite \textit{A. Gierzkiewicz} and \textit{P. Zgliczyński}, Commun. Nonlinear Sci. Numer. Simul. 101, Article ID 105891, 13 p. (2021; Zbl 1472.34060) Full Text: DOI arXiv
Kapela, Tomasz; Mrozek, Marian; Wilczak, Daniel; Zgliczyński, Piotr CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems. (English) Zbl 1473.37004 Commun. Nonlinear Sci. Numer. Simul. 101, Article ID 105578, 26 p. (2021). MSC: 37-04 37Mxx 65Pxx PDFBibTeX XMLCite \textit{T. Kapela} et al., Commun. Nonlinear Sci. Numer. Simul. 101, Article ID 105578, 26 p. (2021; Zbl 1473.37004) Full Text: DOI arXiv
Kalita, Piotr; Zgliczyński, Piotr On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditions. (English) Zbl 1454.37074 Proc. R. Soc. Edinb., Sect. A, Math. 150, No. 4, 2025-2054 (2020). Reviewer: Jörg Härterich (Bochum) MSC: 37L30 37L05 37L15 35B35 35B40 35K55 35B41 PDFBibTeX XMLCite \textit{P. Kalita} and \textit{P. Zgliczyński}, Proc. R. Soc. Edinb., Sect. A, Math. 150, No. 4, 2025--2054 (2020; Zbl 1454.37074) Full Text: DOI arXiv
Wilczak, Daniel; Zgliczyński, Piotr A geometric method for infinite-dimensional chaos: symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line. (English) Zbl 1439.35218 J. Differ. Equations 269, No. 10, 8509-8548 (2020). MSC: 35K35 35B30 35B40 65G30 35B10 35B45 65N30 PDFBibTeX XMLCite \textit{D. Wilczak} and \textit{P. Zgliczyński}, J. Differ. Equations 269, No. 10, 8509--8548 (2020; Zbl 1439.35218) Full Text: DOI arXiv
Szczelina, Robert; Zgliczyński, Piotr Algorithm for rigorous integration of delay differential equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation. (English) Zbl 1402.65050 Found. Comput. Math. 18, No. 6, 1299-1332 (2018). MSC: 65L03 34K13 34K28 65G30 PDFBibTeX XMLCite \textit{R. Szczelina} and \textit{P. Zgliczyński}, Found. Comput. Math. 18, No. 6, 1299--1332 (2018; Zbl 1402.65050) Full Text: DOI arXiv
Czechowski, Aleksander; Zgliczyński, Piotr Existence of periodic solutions of the Fitzhugh-Nagumo equations for an explicit range of the small parameter. (English) Zbl 1360.34069 SIAM J. Appl. Dyn. Syst. 15, No. 3, 1615-1655 (2016). Reviewer: Nikola Popovic (Edinburgh) MSC: 34C05 34C25 34E13 65G20 92C20 PDFBibTeX XMLCite \textit{A. Czechowski} and \textit{P. Zgliczyński}, SIAM J. Appl. Dyn. Syst. 15, No. 3, 1615--1655 (2016; Zbl 1360.34069) Full Text: DOI arXiv
Cyranka, Jacek; Zgliczyński, Piotr Stabilizing effect of large average initial velocity in forced dissipative PDEs invariant with respect to Galilean transformations. (English) Zbl 1347.35041 J. Differ. Equations 261, No. 8, 4648-4708 (2016). MSC: 35B40 35Q30 35B41 35B27 PDFBibTeX XMLCite \textit{J. Cyranka} and \textit{P. Zgliczyński}, J. Differ. Equations 261, No. 8, 4648--4708 (2016; Zbl 1347.35041) Full Text: DOI arXiv
Cyranka, Jacek; Zgliczyński, Piotr Existence of globally attracting solutions for one-dimensional viscous Burgers equation with nonautonomous forcing – a computer assisted proof. (English) Zbl 1312.65170 SIAM J. Appl. Dyn. Syst. 14, No. 2, 787-821 (2015). MSC: 65M99 35B40 35Q53 37B55 65G40 PDFBibTeX XMLCite \textit{J. Cyranka} and \textit{P. Zgliczyński}, SIAM J. Appl. Dyn. Syst. 14, No. 2, 787--821 (2015; Zbl 1312.65170) Full Text: DOI arXiv
Wójcik, Klaudiusz; Zgliczyński, Piotr Isolating segments, fixed point index, and symbolic dynamics. III: Applications. (English) Zbl 1025.37013 J. Differ. Equations 183, No. 1, 262-278 (2002). Reviewer: Sergei Yu.Pilyugin (St.Peterburg) MSC: 37C25 37B10 34C28 34C37 PDFBibTeX XMLCite \textit{K. Wójcik} and \textit{P. Zgliczyński}, J. Differ. Equations 183, No. 1, 262--278 (2002; Zbl 1025.37013) Full Text: DOI
Misiurewicz, Michał; Zgliczyński, Piotr Topological entropy for multidimensional perturbations of one-dimensional maps. (English) Zbl 1090.37507 Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, No. 5, 1443-1446 (2001). MSC: 37B40 37E05 PDFBibTeX XMLCite \textit{M. Misiurewicz} and \textit{P. Zgliczyński}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, No. 5, 1443--1446 (2001; Zbl 1090.37507) Full Text: DOI
Zgliczyński, Piotr On periodic points for systems of weakly coupled 1-dim maps. (English) Zbl 1076.37505 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 46, No. 7, 1039-1062 (2001). Reviewer: Sophia L. Kalpazidou (Thessaloniki) MSC: 37C25 37E05 37B10 PDFBibTeX XMLCite \textit{P. Zgliczyński}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 46, No. 7, 1039--1062 (2001; Zbl 1076.37505) Full Text: DOI
Wójcik, Klaudiusz; Zgliczyński, Piotr Isolating segments, fixed point index, and symbolic dynamics. II: Homoclinic solutions. (English) Zbl 0996.37020 J. Differ. Equations 172, No. 1, 189-211 (2001). Reviewer: Sergei Yu.Pilyugin (St.Peterburg) MSC: 37C29 34C37 37C25 37D45 PDFBibTeX XMLCite \textit{K. Wójcik} and \textit{P. Zgliczyński}, J. Differ. Equations 172, No. 1, 189--211 (2001; Zbl 0996.37020) Full Text: DOI
Arioli, Gianni; Zgliczyński, Piotr Symbolic dynamics for the Hénon-Heiles Hamiltonian on the critical level. (English) Zbl 1018.37006 J. Differ. Equations 171, No. 1, 173-202 (2001). Reviewer: Simos Ichtiaroglou (Thessaloniki) MSC: 37B10 37J45 70H05 70H07 PDFBibTeX XMLCite \textit{G. Arioli} and \textit{P. Zgliczyński}, J. Differ. Equations 171, No. 1, 173--202 (2001; Zbl 1018.37006) Full Text: DOI
Wójcik, Klaudiusz; Zgliczyński, Piotr Isolating segments, fixed point index, and symbolic dynamics. (English) Zbl 0953.34034 J. Differ. Equations 161, No. 2, 245-288 (2000). Reviewer: Sergei Yu.Pilyugin (St.Peterburg) MSC: 34C28 37C25 37B30 37B10 PDFBibTeX XMLCite \textit{K. Wójcik} and \textit{P. Zgliczyński}, J. Differ. Equations 161, No. 2, 245--288 (2000; Zbl 0953.34034) Full Text: DOI
Galias, Z.; Zgliczyński, P. Computer assisted proof of chaos in the Lorenz equations. (English) Zbl 0941.37018 Physica D 115, No. 3-4, 165-188 (1998). MSC: 37D45 37N30 34C28 37M99 37-04 37C25 PDFBibTeX XMLCite \textit{Z. Galias} and \textit{P. Zgliczyński}, Physica D 115, No. 3--4, 165--188 (1998; Zbl 0941.37018) Full Text: DOI
Szymczak, Andrzej; Wójcik, Klaudiusz; Zgliczyński, Piotr On the discrete Conley index in the invariant subspace. (English) Zbl 0956.37009 Topology Appl. 87, No. 2, 105-115 (1998). Reviewer: Marian Mrozek (Kraków) MSC: 37B30 54H20 PDFBibTeX XMLCite \textit{A. Szymczak} et al., Topology Appl. 87, No. 2, 105--115 (1998; Zbl 0956.37009) Full Text: DOI