Marian Mrozek
Papers 
(preprints of titles marked in blue are downloadable in PDF or PostScript form)

• 63. M. Mrozek, B. Batko,
  Coreduction Homology Algorithm
  published version in: Discrete and Computational Geometry, accepted.
• 62. M. Mrozek, P. Pilarczyk, N. Żelazna,
  Homology Algorithm Based on Acyclic Subspace
  published version in: Computers and Mathematics, accepted.
• 61. M. Mrozek,
  The Method of Topological Sections in the Rigorous Numerics of Dynamical Systems
  published version in: Canadian Applied Mathematics Quarterly, 14(2006), 209-222.
• 60. M. Mrozek, R. Srzednicki,
  Conley index of Poincare maps in isolating segments
  published version in: Nonlinear Analysis, Theory, Methods and Applications, accepted.
• 59. M. Mrozek,
  Index Pairs Algorithms
  published version in: Foundations of Computational Mathematics, 6(2006), 457-493.
• 58. Bogdan Batko, M. Mrozek,
  The Euler-Poincare characteristic of index maps
  published version in: Topology and its Applications, 154(2007), 859-866.
• 57. Tomasz Kaczynski, M. Mrozek, Anik Trahan,
  Ideas from Zariski topology in the study of cubical sets, cubical maps, and their homology
  published version in: Canadian J. Math. 59(2007), 1008-1028.
• 56. K. Mischaikow, M. Mrozek, P. Pilarczyk,
  Graph Approach to the Computation of the Homology of Continuous Maps,
  published version in: Foundations of Computational Mathematics, 5(2005), 199-229
• 55. M. Mrozek, K. Wójcik,
  A discrete version of a geometric method for detecting chaotic dynamics,
  published version in: Topology and its Applications, 152(2005), 70-82.
• 54. T. Kaczynski, K. Mischaikow, M. Mrozek,
  Computing Homology,
  published version in: Homotopy, Homology and Applications, 5(2003), 233-256.
• 53. M. Mrozek, P. Pilarczyk,
  The Conley Index and Rigorous Numerics of Attracting Periodic Orbits,
  published version in: Variational and Topological Methods in the Study of Nonlinear Phenomena, V. Benci et al. Editors, Progress in Nonlinear Differential Equations and Their Applications, Vol. 49, Birkhauser, Boston, Basel, Berlin 2002.
• 52. K. Mischaikow, M. Mrozek,
  The Conley Index Theory,
  published version in: Handbook of Dynamical Systems III: Towards Applications, Editors: B. Fiedler, G. Iooss, N. Kopell, Elsevier Science B. V., Singapore 2002, Editor: B. Fiedler, 393-460.
• 51. M. Mrozek, P. Zgliczyński,
  Set arithmetic and the enclosing problem in dynamics,
  published version in: Annales Polonici Mathematici, 74(2000), 237-259.
• 50. M. Mrozek, J. Reineck and R. Srzednicki,
  On a Generalization of the Conley index,
  published version in: Conley index theory, Banach Center Publications, 47(1999), 157-171.
• 49. M. Mrozek,
  Construction and properties of the Conley index,
  published version in: Conley index theory, Banach Center Publications, 47(1999), 29-40.
• 48. K. Mischaikow, M. Mrozek, J. Reiss and A. Szymczak,
  Construction of Symbolic Dynamics from Experimental Time Series,
  published version in: Physical Review Letters, 82(1999), p. 1144.
• 47. K. Mischaikow, M. Mrozek,  J. Reineck, Singular Index Pairs,
  published version in: Proceedings of the Conference "Topological Methods in Differential Equations",
  Univ. Iag. Acta Math., 36(1998), 223-226.
• 46. M. Mrozek,
  Algorithms and the Conley index theory,
  published version in: Proceedings of the Conference "Topological Methods in Differential Equations",
  Univ. Iag. Acta Math., 36(1998), 227-230.
• 45. M. Mrozek and J. Urbaniec,
  Evolution of Mathematical Proof,
  published version in: Foundations of Science, 2(1997), 77-85.
• 44. T. Kaczynski M. Mrozek and M. Slusarek,
  Homology Computation by Reduction of Chain Complexes,
  published version in: Computers and Mathematics, 35(1998), no. 4, 59--70.
• 43. M. Mrozek and M. Zelawski,
  Heteroclinic connections in the Kuramoto-Sivashinsky equation,
  published version in: Reliable Computing, 3(1997), 277-285.
• 42. Mrozek, M.
  The Conley Index and Rigorous Numerics,
  published version in: Nonlinear Analysis and Boundary Value Problems for Ordinary Differential Equations, CISM Courses ans Lectures Vol. 371, Springer Verlag, Wien, 1996, p.175-196.
• 41. Mrozek, M.
  Inheritable properties and computer assisted proofs in dynamics,
  published version in: Scientific Computing and validated numerics, G. Alefeld, A. Frommer and B. Lang editors, Akademie Verlag, Berlin, pp. 245-253.
• 40. Mrozek, M.
  An algorithmic approach to the Conley index theory
  ( Version revised after publication is here ),
  published version in: J. Dyn. Diff. Equ. 11(1999), 711-734.
  
• 39. Mischaikow, K. and Mrozek, M. and Szymczak, A.
  Chaos in the Lorenz equations: a computer assisted proof. Part III: the classical parameter values,
  published version in: J. Diff. Equ. 169(2001), 17-56.
• 38. Mrozek, M.
  Rigorous numerics of chaotic dynamical suystems,
  published version in: Chaos - the Interplay between Stochastic and Deterministic Behaviour, P. Garbaczewski ... (eds),
  Lect. Notes in Physics, 457(), 283-296.
• 37. Mrozek, M. and Reineck, J. and Srzednicki, R.
  The Conley index over a circle,
  published version in: J. Dynamics and Differential Equations, 12(2000), 385--409.
• 36. Mrozek, M. and Reineck, J. and Srzednicki, R.
  The Conley index over a base,
  published version in: Trans. AMS 352(2000), 4171-4194.
• 35. Kaczynski, T. and Mrozek, M.
  Connected simple systems and the Conley functor,
  published version in: Topol. Methods Nonlin. Anal., 10(1997), 183-193.
• 34. Mrozek, M.
  Rigorous error analysis of numerical algorithms via symbolic computations,
  published version in: J. Symb. Comp. 22(1996),435-458.
• 33. Mischaikow, K. and Mrozek, M.
  Chaos in the Lorenz equations: a computer assisted proof. Part II: details, (with figures, zipped)
  published version in: Mathematics of Computation, 67(1998), 1023-1046.
• 32. Mischaikow, K. and Mrozek, M. and Reineck, J.
  Singular index pairs,
  published version in: J. Dyn. Diff. Equ. 11(1999), 399-426.
• 31. Mrozek, M.
  Topological invariants, multivalued maps and computer assisted proofs, (with figures, zipped)
  published version in: Computers & Mathematics, 32(1996),83-104. (Click here for a no-figures version)
• 30. Kaczynski, T. and Mrozek, M.
  Stable index pairs for discrete dynamical systems,
  published version in: Bulletin Canadian Math. Soc., 40(1997), 448-455.
• 29. Mrozek, M.
  From the Theorem of Ważewski to computer assisted proofs in dynamics,
  published version in: Panoramas of Mathematics, Banach Center Publications, 34, 105-120.
• 28. Mischaikow, K. and Mrozek, M.
  Chaos in Lorenz equations: a computer assisted proof,
  published version in: Bull. Amer. Math. Soc. (N.S.), 33(1995), 66-72.
• 27. McCord, Ch. and Mischaikow, K. and Mrozek, M.
  Zeta Functions, Periodic Trajectories and the Conley Index,
  published version in: J. Diff. Equ, 121(1995), 258-292.
• 26. Kaczynski, T. and Mrozek, M.
  Conley index for discrete multivalued dynamical systems,
  published version in: Topology & its Appl., 65(1995), 83-96.
• 25. Mischaikow, K. and Mrozek, M.
  Isolating neighborhoods and chaos,
  published version in: Jap. J. Ind. & Appl. Math., 12(1995), 205-236.
• 24. Mrozek, M.
  Shape index and other indices of Conley type for continuous maps in locally compact metric spaces,
  published version in: Fundamenta Mathematicae, 145(1994), 15-37.
• 23. Mrozek, M. and Srzednicki, R.
  On time-duality of the Conley index,
  Results in Mathematics, 24(1993), 161-167.
• 22. Degiovanni, M. and Mrozek, M.
  The Conley index for maps in absence of compactness,
  Proc. Royal Soc. Edinburgh, 123A(1993), 75-94.
• 21. Mrozek, M. and Rybakowski, K.P.
  Discretized ordinary differential equations and the Conley index,
  J. of Dynamics and Differential Equations, 4(1992), 57-63.
• 20. Mrozek, M. and Rybakowski, K.P.
  Nontrivial full bounded solutions of time-periodic semilinear PDEs,
  Proc. Roy. Soc. Edinburgh, 117A(1991), 305-315.
• 19. Mrozek, M.
  The Conley index on compact ANR's is of finite type,
  Results in Mathematics, 18(1990), 306-313.
• 18. Mrozek, M. and Rybakowski, K.P.
  A cohomological Conley index for maps on metric spaces,
  Journal of Diff. Equations, 90(1991), 143-171.
• 17. Mrozek, M.
  Normal Functors and Retractors in Categories of Endomorphisms,
  Univ. Iag. Acta Math., 29(1992), 181-198.
• 16. Mrozek, M.
  The Morse Equation in Conley's Index Theory for Homeomorphisms,
  Topology and its Applications, 38(1991), 45-60.
• 15. Mrozek, M.
  Open index pairs, the fixed point index and rationality of zeta functions,
  Erg. Th. and Dyn. Syst., 10(1990), 555-564.
• 14. Mrozek, M.
  A cohomological index of Conley type for multivalued admissible flows,
  J. Diff. Equations, 84(1990), 15-51.
• 13. Mrozek, M.
  Leray Functor and the Cohomological Conley Index for Discrete Time Dynamical Systems,
  Transactions of the Amer. Math. Soc., 318(1990), 149-178.
• 12. Mrozek, M.
  Index pairs and the Fixed Point Index for Semidynamical Systems with Discrete Time,
  Fund. Mathematicae, 133(1989), 177-192.
• 11. Mrozek, M. and Srzednicki, R.
  The Continuity Axiom in Multi-Valued Dynamical Systems,
  Rivista di Matematica Pura ed Applicata, 3(1988), 87-97.
• 10. Mrozek, M.
  Some Remarks on the Garay's Conjecture,
  Acta Math. Hungarica, 57(1991), 53-59.
• 9. Mrozek, M.
  Strongly Isolating Invariant Sets and Strongly Isolating Blocks,
  Bull. Acad. Pol. Sc. Ser. Sci. Math., 35(1987), 1-2.
• 8. Mrozek, M.
  Transitively Reduced and Transitively Closed Event Networks,
  Networks, 19(1989), 47-72.
• 7. Mrozek, M.
  A Note on Minimum-Dummy-Activities PERT Networks,
  RAIRO Rech. Oper., 18(1984), 415-421.
• 6. Mrozek, M. and Zaionc, M.
  A Computer Model of Evolution and Ecological Processes,
  Modell. Sim. and Control, 1(1984), 59-63.
• 5. Mrozek, M.
  Periodic and Stationary Trajectories of Flows and Ordinary Differential Equations,
  Univ. Iag. Acta Math., 27(1988), 29-37.
• 4. Mrozek, M.
  The Fixed Point Index of a Translation Operator of a Semiflow,
  Univ. Iag. Acta Math., 27(1988), 13-22.
• 3. Mrozek, M. and Zaionc, M.
  Simulation model of evolution in a simplified ecological system,
  Wiad. Ekol., 27(1981), 49-59.
• 2. Mrozek, M.
  Generalized Inverse of a Finite Graph,
  Fund. Inform. , 4(1981), 499-509.
• 1. Mrozek, M.
  Inverse Limits of Torus-Groups and Minimal Sets of some Almost Periodic Continuous Flows -,
  Zesz. Nauk. UJ, Pr. Mat., 21(1979), 29-50.