papers

Marian Mrozek
Publications
(preprints of titles marked in blue are downloadable in PDF or PostScript form)
Books and book chapters

4. M. Mrozek,
Topological Dynamics: Rigorous Numerics via Cubical Homology,
in: Advances in Applied and Computational Topology: AMS Short Course Computational Topology,
Proceedings of Symposia in Applied Mathematics 70 (A. Zomorodian, ed.) , American Mathematical Society, 2011.
3. T. Kaczynski, K. Mischaikow, and M. Mrozek,
Computational Homology,
Applied Mathematical Sciences 157, Springer-Verlag, 2004.
2. K. Mischaikow, M. Mrozek,
The Conley Index, in: Handbook of Dynamical Systems II: Towards Applications,
(B. Fiedler, ed.) North-Holland, 2002.
1. K. Mischaikow, M. Mrozek and P. Zgliczyński (eds.),
Conley Index Theory, Banach Center Publications, Vol. 47,
Institute of Mathematics, Polish Academy of Sciences, 1999.

Papers

109. M. Lipiński, K. Mischaikow and M. Mrozek.
Morse predecomposition of an invariant set.
Preprint 2023, arXiv:2312.08013 [math.DS]
108. Herbert Edelsbrunner and Marian Mrozek.
The Depth Poset of a Filtered Lefschetz Complex.
Preprint 2023, arXiv:2311.14364 [math.AT]
107. Jonathan Ariel Barmak, Marian Mrozek, and Thomas Wanner.
Conley index for multivalued maps on finite topological spaces.
Preprint 2023, arXiv:2310.03099 [math.DS]
106. T. Dey, M. Lipiński, M. Mrozek, and R. Slechta}.
Computing Connection Matrices via Persistence-like Reductions.
Preprint 2023, arXiv:2303.02549 [math.AT]
published version in:
SIAM Journal on Applied Dynamical Systems, accepted
105. M. Przybylski, M. Mrozek and J. Wiseman}.
The Szymczak functor and shift equivalence on the category of finite sets and finite relations,
Preprint 2023, arXiv:2203.08525 [math.DS]
published version in:
Journal of Dynamics and Differential Equations, accepted
104. T. Dey, M. Lipiński, M. Mrozek, and R. Slechta.
Tracking Dynamical Features via Continuation and Persistence,
published version in:
38th International Symposium on Computational Geometry (SoCG 2020)
Leibniz International Proceedings in Informatics (LIPIcs) 224(2022), 35:1-35:17
103. T. Dey, M. Mrozek, and R. Slechta
Persistence of the Conley-Morse Graph in Combinatorial Dynamical Systems.
SIAM Journal on Applied Dynamical Systems 21(2022), 817--839.
102. L. Fribourg, E. Goubault, S. Mohamed, M. Mrozek and S. Putot.
A topological method for finding invariant sets of continuous systems.
Information and Computation 277(2021), 104581(1--12). DOI: 10.1016/j.ic.2020.104581
101. M. Mrozek, R. Srzednicki, J. Thorpe and Th. Wanner.
Combinatorial vs. classical dynamics: Recurrence.
Communications in Nonlinear Science and Numerical Simulation 108(2022), 106226(1--30).
100. T. Kapela, M. Mrozek, D. Wilczak, and P. Zgliczyński.
CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems.
Communications in Nonlinear Science and Numerical Simulation 101(2021), 105578(1-18).
99. M. Mrozek, and Th. Wanner.
Connection matrices in combinatorial topological dynamics.
Preprint 2021, arXiv:2103.04269 [math.DS]
98. M. Mrozek, and Th. Wanner.
Creating Semiflows on Simplicial Complexes from Combinatorial Vector Fields.
published version in:
Journal of Differential Equations 304(2021), 375-434. DOI: 10.1137/19M1254404.
97. M. Lipiński, J. Kubica, M. Mrozek, and Th. Wanner.
Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces,
Journal of Applied and Computational Topology 7(2023) 139-184. DOI: 10.1007/s41468-022-00102-9
Preprint 2020, arXiv:1911.12698 [math.DS]
96. T. Dey, M. Mrozek, and R. Slechta.
Persistence of the Conley index in combinatorial dynamical systems,
published version in:
36th International Symposium on Computational Geometry (SoCG 2020)
Leibniz International Proceedings in Informatics (LIPIcs) 164(2020), 37:1-37:17.
95. B. Batko, K. Mischaikow, M. Mrozek, and M. Przybylski.
Conley index approach to sampled dynamics,
published version in:
SIAM Journal on Applied Dynamical Systems 19(2020), 665-704. DOI: 10.1137/19M1254404.
94. J.A. Barmak, M. Mrozek, and Th. Wanner.
A Lefschetz fixed point theorem for multivalued maps of finite spaces,
published version in:
Mathematische Zeitschrfit 18(2020), 1477-1479. DOI: 10.1007/s00209-019-02333-6
93. T. Dey, M. Juda, T. Kapela, J. Kubica, M. Lipiński, and M. Mrozek.
Persistent Homology of Morse Decompositions in Combinatorial Dynamics,
published version in:
SIAM Journal on Applied Dynamical Systems 18(2019), 510-530. DOI: 10.1137/18M1198946.
92. B. Batko, T. Kaczynski, M. Mrozek, and Th. Wanner.
Linking combinatorial and classical dynamics: Conley index and Morse decompositions,
published version in:
Foundations of Computational Mathematics 20(2020) 967-1012. DOI: 10.1007/s10208-020-09444-1
91. U. Bauer, H. Edelsbrunner, G. Jabłoński, M. Mrozek.
Čech-Delaunay gradient flow and homology inference for self-maps,
published version in:
Journal of Applied and Computational Topology 4(2020), 455-480. DOI: 10.1007/s41468-020-00058-8
90. M. Ethier G. Jabłoński and M. Mrozek,
Finding Eigenvalues of Self-maps with the Kronecker Canonical Form,
published version in:
I.S. Kotsireas and E. Martínez-Moro (eds.), Applications of Computer Algebra,
Springer Proceedings in Mathematics and Statistics 198(2017), Springer.
89. M. Mrozek,
Conley-Morse-Forman theory for combinatorial multivector fields on Lefschetz complexes,
published version in:
Foundations of Computational Mathematics 17(2017), 1585--1633. DOI: 10.1007/s10208-016-9330-z.
88. L. Fribourg, E. Goubault, S. Mohamed, M. Mrozek and S. Putot.
A Topological Method for Finding Invariants of Continuous Systems,
in: RP'15, Lecture Notes in Computer Science 9328(2015), 63-75.
87. B. Batko, M. Mrozek,
Weak index pairs and the Conley index for discrete multivalued dynamical systems,
published version in:
SIAM Journal on Applied Dynamical Systems 15(2016), 1143-–1162.
86. P. Brendel, G. Ellis, M. Juda, M. Mrozek.
Fundamental Group Algorithm for low dimensional tesselated CW complexes,
preprint 2015, arXiv:1507.03396 [math.AT].
85. T. Kaczynski, M. Mrozek, and Th. Wanner,
Towards a Formal Tie Between Combinatorial and Classical Vector Field Dynamics,
preprint 2014, IMA Preprint Series #2443.
84. K. Mischaikow, M. Mrozek, F. Weilandt,
Discretization strategies for computing Conley indices and Morse decompositions of flows,
preprint 2015, arXiv:1511.04426 [math.DS].
83. M. Mrozek, R. Srzednicki, F. Weilandt,
A topological approach to the algorithmic computation of the Conley index of Poincar\'e operators,
published version in:
SIAM Journal on Applied Dynamical Systems 14(2015), 1348–-1386.
82. H. Edelsbrunner, G. Jabłoński, M. Mrozek,
The Persistent Homology of a Self-map,
published version in:
Foundations of Computational Mathematics, 15(2015), 1213-1244.
81. P. Brendel, P. Dłotko, G. Ellis, M. Juda, M. Mrozek,
Computing fundamental groups from point clouds,
published version in:
Applicable Algebra in Engineering, Communication and Computing, 26(2015), 27-48.
80. M. Juda, M. Mrozek,
CAPD::RedHom v2 - Homology Software Based on Reduction Algorithms,
in: Mathematical Software – ICMS 2014, Lecture Notes in Computer Science 8592(2014), 160-166.
79. S. Harker, K. Mischaikow, M. Mrozek, V. Nanda,
Discrete Morse Theoretic Algorithms for Computing Homology of Complexes and Maps,
published version in: Foundations of Computational Mathematics, 14(2014) 151-184, DOI:10.1007/s10208-013-9145-0
78. T. Kaczynski, M. Mrozek,
Cubical Cohomology Ring: Algorithmic Approach,
published version in: Foundations of Computational Mathematics, 13(2013) 789-818, DOI 10.1007/s10208-012-9138-4.
77. H. Wagner, P. Dłotko, M. Mrozek,
Computational topology in text mining,
published version in: Lecture Notes in Computer Science 7309(2012), 68-78, DOI: 10.1007/978-3-642-30238-1_8.
76. P. Brendel, P. Dłotko, M. Mrozek, N. Żelazna,
Homology Computations via Acyclic Subspace,
published version in: Lecture Notes in Computer Science 7309(2012), 117-127, DOI: 10.1007/978-3-642-30238-1_13.
75. Barbara Gryglewska, Mirosław Nęcki, Marcin Żelawski, Marcin Cwynar, Tomasz Baron, Marian Mrozek, Tomasz Grodzicki,
Fractal dimensions of skin microcirculation flow in subjects with familial predisposition or newly diagnosed hypertension,
published version in: Cardiology Journal, 11.1(2011), 26–32.
74. P. Dłotko, R. Ghrist, M. Juda, M. Mrozek,
Distributed computation of coverage in sensor networks by homological methods,
published version in: Applicable Algebra in Engineering, Communication and Computing, 23(2012), 29--58, DOI:10.1007/s00200-012-0167-7.
73. P. Dłotko, T. Kaczynski, M. Mrozek
Computing The Cubical Cohomology Ring,
published version in: Proceedings of the 3rd International Workshop on Computational Topology in Image Context, Chipiona, Spain, November 2010 (Rocio Gonzalez Diaz Pedro Real Jurado (Eds.)), Image A Vol. 3(2010), 137–142.
72. S. Harker, K. Mischaikow, M. Mrozek, V. Nanda, H. Wagner, M. Juda, P. Dłotko
The Efficiency of a Homology Algorithm based on Discrete Morse Theory and Coreductions,
published version in: Proceedings of the 3rd International Workshop on Computational Topology in Image Context, Chipiona, Spain, November 2010 (Rocio Gonzalez Diaz Pedro Real Jurado (Eds.)), Image A Vol. 1(2010), 41-47.
71. P. Dłotko, T. Kaczynski, M. Mrozek, Th. Wanner,
Coreduction Homology Algorithm for Regular CW-Complexes,
published version in: Discrete and Computational Geometry, 46(2011), 361-388, DOI: 10.1007/s00454-010-9303-y.
70. M. Mrozek, M. Żelawski, A. Gryglewski, S. Han, A. Krajniak,
Homological methods for extraction and analysis of linear features in multidimensional images,
published version in: Pattern Recognition, 45(2012), 285-298, DOI:10.1016/j.patcog.2011.04.020.
69. M. Mrozek, Th. Wanner
Coreduction homology algorithm for inclusions and persistent homology,
published version in: Computers and Mathematics with Applications, 60.10(2010), 2812-2833, DOI: 10.1016/j.camwa.2010.09.036.
68. M. Juda, M. Mrozek,
$Z_2$-Homology of weak $(n-2)$-faceless $n$-pseudomanifolds may be computed in $O(n)$ time
published version in: Topological Methods in Nonlinear Analysis, 40(2012), 137-159.
67. M. Mrozek,
Cech Type Approach to Computing Homology of Maps,
published version in: Discrete and Computational Geometry, 44.3(2010), 546-576, DOI: 10.1007/s00454-010-9255-2.
66. M. Mrozek, B. Batko
Homology of representable sets,
published version in: Annales Polonici Mathematici 97.3(2010), 243-252.
65. M. Mrozek, M. Żelawski, A. Krajniak, A. Gryglewski, S. Han, Homological methods in feature extraction of multidimensional images,
published version in: Proceedings of the 2009 2nd International Congress on Image and Signal Processing, Tianjin, Chiny, IEEE 2009, 1061-1066.
64. M. Mrozek, R. Srzednicki,
Topological approach to rigorous numerics of chaotic dynamical systems with strong expansion,
published version in: Foundations of Computational Mathematics, DOI: 10.1007/s10208-009-9053-5.
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 with Applications, 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 with Applications, 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 systems,
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.