Marian Mrozek
Publications
(preprints of titles marked in blue are downloadable in PDF or PostScript form)
Book
- 1. T. Kaczynski, K. Mischaikow, and M. Mrozek,
Computational Homology,
Applied Mathematical Sciences 157, Springer-Verlag, 2004.
Papers
- 65. M. Mrozek,
Cech Type Approach to Computing Homology of Maps, revised preprint.
- 64. M. Mrozek, R. Srzednicki,
Topological approach to rigorous numerics of chaotic dynamical systems with strong expansion, preprint.
- 63. M. Mrozek, B. Batko,
Coreduction Homology Algorithm
published version in: Discrete and Computational Geometry, 41(2009), 96-118.
- 62. M. Mrozek, P. Pilarczyk, N. Żelazna,
Homology Algorithm Based on Acyclic Subspace
published version in: Computers and Mathematics, 55(2008), 2395–2412.
- 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, 70(2009) 2123–2131.
- 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.