## Mrozek, Marian

Compute Distance To:
 Author ID: mrozek.marian Published as: Mrozek, Marian; Mrozek, M.
 Documents Indexed: 93 Publications since 1979, including 1 Book 1 Contribution as Editor Reviewing Activity: 50 Reviews Co-Authors: 44 Co-Authors with 64 Joint Publications 676 Co-Co-Authors
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### Co-Authors

 30 single-authored 15 Mischaikow, Konstantin 11 Kaczynski, Tomasz 9 Srzednicki, Roman 7 Wanner, Thomas 6 Batko, Bogdan 5 Dłotko, Paweł 5 Juda, Mateusz 5 Reineck, James F. 3 Jablonski, Grzegorz 3 Pilarczyk, Paweł 3 Rybakowski, Krzysztof P. 3 Zgliczyński, Piotr 2 Brendel, Piotr 2 Dey, Tamal Krishna 2 Edelsbrunner, Herbert 2 Fribourg, Laurent 2 Goubault, Eric 2 Kapela, Tomasz 2 Mohamed, Sameh 2 Putot, Sylvie 2 Weilandt, Frank 2 Ẓelazna, Natalia 1 Barmak, Jonathan Ariel 1 Bauer, Ulrich 1 Degiovanni, Marco 1 Ellis, Graham J. 1 Ethier, Marc 1 Ghrist, Robert W. 1 Harker, Shaun 1 Kubica, Jacek 1 Lipiński, Michał 1 McCord, Christopher K. 1 Nanda, Vidit 1 Przybylski, Mateusz 1 Slechta, Ryan 1 Ślusarek, Maciej 1 Szymczak, Andrzej 1 Thorpe, Justin 1 Trahan, Anik 1 Urbaniec, Jacek 1 Wagner, Hubert 1 Wilczak, Daniel 1 Wójcik, Klaudiusz 1 Żelawski, Marcin
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### Serials

 8 Foundations of Computational Mathematics 5 Journal of Differential Equations 5 SIAM Journal on Applied Dynamical Systems 4 Computers & Mathematics with Applications 4 Topology and its Applications 4 Journal of Dynamics and Differential Equations 3 Discrete & Computational Geometry 3 Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Acta Mathematica 2 Annales Polonici Mathematici 2 Fundamenta Mathematicae 2 Results in Mathematics 2 Transactions of the American Mathematical Society 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Applicable Algebra in Engineering, Communication and Computing 2 Topological Methods in Nonlinear Analysis 2 Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica 2 Communications in Nonlinear Science and Numerical Simulation 2 Journal of Computational Dynamics 1 Mathematics of Computation 1 Canadian Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Mathematische Zeitschrift 1 Networks 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 RAIRO. Recherche Opérationnelle 1 Annales Societatis Mathematicae Polonae. Series IV 1 Ergodic Theory and Dynamical Systems 1 Acta Mathematica Hungarica 1 Journal of Symbolic Computation 1 Information and Computation 1 Rivista di Matemàtica Pura ed Applicata 1 Japan Journal of Industrial and Applied Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Bulletin of the Polish Academy of Sciences, Mathematics 1 The Canadian Applied Mathematics Quarterly 1 Reliable Computing 1 Homology, Homotopy and Applications 1 Foundations of Science 1 Applied Mathematical Sciences 1 Banach Center Publications 1 Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Prace Matematyczne 1 Journal of Applied and Computational Topology
all top 5

### Fields

 57 Dynamical systems and ergodic theory (37-XX) 32 Algebraic topology (55-XX) 30 General topology (54-XX) 22 Numerical analysis (65-XX) 18 Ordinary differential equations (34-XX) 18 Computer science (68-XX) 11 Manifolds and cell complexes (57-XX) 6 Convex and discrete geometry (52-XX) 4 Category theory; homological algebra (18-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Operations research, mathematical programming (90-XX) 2 General and overarching topics; collections (00-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Partial differential equations (35-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Difference and functional equations (39-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX)

### Citations contained in zbMATH Open

78 Publications have been cited 925 times in 437 Documents Cited by Year
Computational homology. Zbl 1039.55001
Kaczynski, Tomasz; Mischaikow, Konstantin; Mrozek, Marian
2004
Chaos in the Lorenz equations: A computer-assisted proof. Zbl 0820.58042
Mischaikow, Konstantin; Mrozek, Marian
1995
Leray functor and cohomological Conley index for discrete dynamical systems. Zbl 0686.58034
Mrozek, Marian
1990
Conley index. Zbl 1035.37010
Mischaikow, Konstantin; Mrozek, Marian
2002
Isolating neighborhoods and chaos. Zbl 0840.58033
Mischaikow, Konstantin; Mrozek, Marian
1995
Chaos in the Lorenz equations: A computer assisted proof. II: Details. Zbl 0913.58038
Mischaikow, Konstantin; Mrozek, Marian
1998
Conley index for discrete multi-valued dynamical systems. Zbl 0843.54042
Kaczynski, T.; Mrozek, Marian
1995
Chaos in the Lorenz equations: A computer assisted proof. III: Classical parameter values. Zbl 0979.37015
Mischaikow, Konstantin; Mrozek, Marian; Szymczak, Andrzej
2001
Homology computation by reduction of chain complexes. Zbl 0904.55004
Kaczýnski, T.; Mrozek, M.; Ślusarek, M.
1998
Discrete Morse theoretic algorithms for computing homology of complexes and maps. Zbl 1387.55010
Harker, Shaun; Mischaikow, Konstantin; Mrozek, Marian; Nanda, Vidit
2014
Coreduction homology algorithm. Zbl 1163.68041
Mrozek, Marian; Batko, Bogdan
2009
Shape index and other indices of Conley type for local maps on locally compact Hausdorff spaces. Zbl 0870.54043
Mrozek, Marian
1994
A cohomological index of Conley type for multi-valued admissible flows. Zbl 0703.34019
Mrozek, Marian
1990
Index pairs algorithms. Zbl 1111.37006
Mrozek, Marian
2006
Graph approach to the computation of the homology of continuous maps. Zbl 1104.55001
Mischaikow, Konstantin; Mrozek, Marian; Pilarczyk, Pawel
2005
Index pairs and the fixed point index for semidynamical systems with discrete time. Zbl 0708.58024
Mrozek, Marian
1989
Zeta functions, periodic trajectories, and the Conley index. Zbl 0833.34045
McCord, Christopher; Mischaikow, Konstantin; Mrozek, Marian
1995
The persistent homology of a self-map. Zbl 1330.55009
Edelsbrunner, Herbert; Jabłoński, Grzegorz; Mrozek, Marian
2015
Topological invariants, multivalued maps and computer assisted proofs in dynamics. Zbl 0861.58027
Mrozek, Marian
1996
A cohomological Conley index for maps on metric spaces. Zbl 0721.58040
Mrozek, Marian; Rybakowski, Krzysztof P.
1991
Coreduction homology algorithm for regular CW-complexes. Zbl 1229.55001
Dłotko, Paweł; Kaczynski, Tomasz; Mrozek, Marian; Wanner, Thomas
2011
An algorithmic approach to the Conley index theory. Zbl 0941.37004
Mrozek, Marian
1999
The Conley index on compact ANR’s is of finite type. Zbl 0723.54038
Mrozek, Marian
1990
Computing homology. Zbl 1028.55001
Kaczynski, Tomasz; Mischaikow, Konstantin; Mrozek, Marian
2003
Homology algorithm based on acyclic subspace. Zbl 1142.15300
Mrozek, Marian; Pilarczyk, Paweł; Ẓelazna, Natalia
2008
Coreduction homology algorithm for inclusions and persistent homology. Zbl 1207.57001
Mrozek, Marian; Wanner, Thomas
2010
Set arithmetic and the enclosing problem in dynamics. Zbl 0967.65113
Mrozek, Marian; Zgliczyński, Piotr
2000
Conley-Morse-Forman theory for combinatorial multivector fields on Lefschetz complexes. Zbl 1384.54023
Mrozek, Marian
2017
The Conley index over a base. Zbl 0967.37011
Mrozek, Marian; Reineck, James F.; Srzednicki, Roman
2000
CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems. Zbl 1473.37004
Kapela, Tomasz; Mrozek, Marian; Wilczak, Daniel; Zgliczyński, Piotr
2021
Persistent homology of Morse decompositions in combinatorial dynamics. Zbl 1415.37058
Dey, Tamal K.; Juda, Mateusz; Kapela, Tomasz; Kubica, Jacek; Lipiński, Michał; Mrozek, Marian
2019
On time-duality of the Conley index. Zbl 0783.34039
Mrozek, Marian; Srzednicki, Roman
1993
Open index pairs, the fixed point index and rationality of zeta functions. Zbl 0696.58044
Mrozek, Marian
1990
Towards a formal tie between combinatorial and classical vector field dynamics. Zbl 1353.37096
Wanner, Thomas; Mrozek, Marian; Kaczynski, Tomasz
2016
CAPD::RedHom v2 – homology software based on reduction algorithms. Zbl 1402.57021
Juda, Mateusz; Mrozek, Marian
2014
Weak index pairs and the Conley index for discrete multivalued dynamical systems. Zbl 1350.54027
Batko, Bogdan; Mrozek, Marian
2016
Linking combinatorial and classical dynamics: Conley index and Morse decompositions. Zbl 1456.37040
Batko, Bogdan; Kaczynski, Tomasz; Mrozek, Marian; Wanner, Thomas
2020
Discretized ordinary differential equations and the Conley index. Zbl 0745.34041
Mrozek, Marian; Rybakowski, Krzysztof P.
1992
Normal functors and retractors in categories of endomorphisms. Zbl 0758.18004
Mrozek, Marian
1992
Singular index pairs. Zbl 0943.34028
Mischaikow, Konstantin; Mrozek, Marian; Reineck, James F.
1999
The Morse equation in Conley’s index theory for homeomorphisms. Zbl 0725.58022
Mrozek, Marian
1991
Topological approach to rigorous numerics of chaotic dynamical systems with strong expansion of error bounds. Zbl 1192.65152
Mrozek, Marian; Srzednicki, Roman
2010
Computing fundamental groups from point clouds. Zbl 1333.57004
Brendel, Piotr; Dłotko, Paweł; Ellis, Graham; Juda, Mateusz; Mrozek, Marian
2015
Distributed computation of coverage in sensor networks by homological methods. Zbl 1300.55001
Dłotko, P.; Ghrist, R.; Juda, M.; Mrozek, M.
2012
Discretization strategies for computing Conley indices and Morse decompositions of flows. Zbl 1373.37043
Weilandt, Frank; Mrozek, Marian; Mischaikow, Konstantin
2016
Čech type approach to computing homology of maps. Zbl 1219.55004
Mrozek, Marian
2010
Periodic and stationary trajectories of flows and ordinary differential equations. Zbl 0684.34046
Mrozek, Marian
1988
The cubical cohomology ring: an algorithmic approach. Zbl 1350.55002
Kaczynski, Tomasz; Mrozek, Marian
2013
Čech-Delaunay gradient flow and homology inference for self-maps. Zbl 1479.55010
Bauer, U.; Edelsbrunner, H.; Jabłoński, G.; Mrozek, M.
2020
The Conley index and rigorous numerics. Zbl 0887.58036
Mrozek, M.
1996
Heteroclinic connections in the Kuramoto-Sivashinsky equation: A computer assisted proof. Zbl 0888.65091
Mrozek, Marian; Żelawski, Marcin
1997
Stable index pairs for discrete dynamical systems. Zbl 0903.54018
Kaczynski, Tomasz; Mrozek, Marian
1997
Connected simple systems and the Conley functor. Zbl 0909.54033
Kaczyński, Tomasz; Mrozek, Marian
1997
Nontrivial full bounded solutions of time-periodic semilinear parabolic PDEs. Zbl 0739.35030
Mrozek, Marian; Rybakowski, Krzysztof P.
1991
Rigorous error analysis of numerical algorithms via symbolic computations. Zbl 0871.65035
Mrozek, Marian
1996
Conley index theory. Zbl 0913.00021
1999
The Conley index for maps in absence of compactness. Zbl 0789.58066
Degiovanni, Marco; Mrozek, Marian
1993
The Conley index and rigorous numerics for attracting periodic orbits. Zbl 1040.37012
Mrozek, M.; Pilarczyk, P.
2002
A Lefschetz fixed point theorem for multivalued maps of finite spaces. Zbl 1436.55001
Barmak, Jonathan Ariel; Mrozek, Marian; Wanner, Thomas
2020
Conley index approach to sampled dynamics. Zbl 1442.37088
Batko, Bogdan; Mischaikow, Konstantin; Mrozek, Marian; Przybylski, Mateusz
2020
The fixed point index of a translation operator of a semiflow. Zbl 0674.54027
Mrozek, Marian
1988
Topological dynamics: rigorous numerics via cubical homology. Zbl 1269.37019
Mrozek, Marian
2012
From the theorem of Ważewski to computer assisted proofs in dynamics. Zbl 0848.34032
Mrozek, Marian
1995
Inheritable properties and computer assisted proofs in dynamics. Zbl 0848.68102
Mrozek, Marian
1996
Homology of representable sets. Zbl 1198.68285
Mrozek, Marian; Batko, Bogdan
2010
The Conley index over the circle. Zbl 0967.37010
Mrozek, Marian; Reineck, James F.; Srzednicki, Roman
2000
Conley index of Poincaré maps in isolating segments. Zbl 1154.37315
Mrozek, Marian; Srzednicki, Roman
2009
The method of topological sections in the rigorous numerics of dynamical systems. Zbl 1136.37363
Mrozek, Marian
2006
Creating semiflows on simplicial complexes from combinatorial vector fields. Zbl 07412665
Mrozek, Marian; Wanner, Thomas
2021
The continuity axiom in multi-valued dynamical systems. Zbl 0689.54024
Mrozek, Marian; Srzednicki, Roman
1988
Homology computations via acyclic subspace. Zbl 1357.68260
Brendel, Piotr; Dłotko, Paweł; Mrozek, Marian; Żelazna, Natalia
2012
A topological approach to the algorithmic computation of the Conley index for Poincaré maps. Zbl 1325.65175
Mrozek, Marian; Srzednicki, Roman; Weilandt, Frank
2015
A topological method for finding invariant sets of continuous systems. Zbl 1471.37018
Fribourg, Laurent; Goubault, Eric; Mohamed, Sameh; Mrozek, Marian; Putot, Sylvie
2015
Some remarks on Garay’s conjecture. Zbl 0749.54007
Mrozek, M.
1991
Rigorous numerics of chaotic dynamical systems. Zbl 0840.65067
Mrozek, Marian
1995
Discrete version of a geometric method for detecting chaotic dynamics. Zbl 1078.37011
Mrozek, Marian; Wójcik, Klaudiusz
2005
The Euler-Poincaré characteristic of index maps. Zbl 1108.37009
Batko, Bogdan; Mrozek, Marian
2007
$$\mathbb{Z}_2$$-homology of weak $$(p-2)$$-faceless $$p$$-pseudomanifolds may be computed in $$O(n)$$ time. Zbl 1276.55003
Juda, Mateusz; Mrozek, Marian
2012
CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems. Zbl 1473.37004
Kapela, Tomasz; Mrozek, Marian; Wilczak, Daniel; Zgliczyński, Piotr
2021
Creating semiflows on simplicial complexes from combinatorial vector fields. Zbl 07412665
Mrozek, Marian; Wanner, Thomas
2021
Linking combinatorial and classical dynamics: Conley index and Morse decompositions. Zbl 1456.37040
Batko, Bogdan; Kaczynski, Tomasz; Mrozek, Marian; Wanner, Thomas
2020
Čech-Delaunay gradient flow and homology inference for self-maps. Zbl 1479.55010
Bauer, U.; Edelsbrunner, H.; Jabłoński, G.; Mrozek, M.
2020
A Lefschetz fixed point theorem for multivalued maps of finite spaces. Zbl 1436.55001
Barmak, Jonathan Ariel; Mrozek, Marian; Wanner, Thomas
2020
Conley index approach to sampled dynamics. Zbl 1442.37088
Batko, Bogdan; Mischaikow, Konstantin; Mrozek, Marian; Przybylski, Mateusz
2020
Persistent homology of Morse decompositions in combinatorial dynamics. Zbl 1415.37058
Dey, Tamal K.; Juda, Mateusz; Kapela, Tomasz; Kubica, Jacek; Lipiński, Michał; Mrozek, Marian
2019
Conley-Morse-Forman theory for combinatorial multivector fields on Lefschetz complexes. Zbl 1384.54023
Mrozek, Marian
2017
Towards a formal tie between combinatorial and classical vector field dynamics. Zbl 1353.37096
Wanner, Thomas; Mrozek, Marian; Kaczynski, Tomasz
2016
Weak index pairs and the Conley index for discrete multivalued dynamical systems. Zbl 1350.54027
Batko, Bogdan; Mrozek, Marian
2016
Discretization strategies for computing Conley indices and Morse decompositions of flows. Zbl 1373.37043
Weilandt, Frank; Mrozek, Marian; Mischaikow, Konstantin
2016
The persistent homology of a self-map. Zbl 1330.55009
Edelsbrunner, Herbert; Jabłoński, Grzegorz; Mrozek, Marian
2015
Computing fundamental groups from point clouds. Zbl 1333.57004
Brendel, Piotr; Dłotko, Paweł; Ellis, Graham; Juda, Mateusz; Mrozek, Marian
2015
A topological approach to the algorithmic computation of the Conley index for Poincaré maps. Zbl 1325.65175
Mrozek, Marian; Srzednicki, Roman; Weilandt, Frank
2015
A topological method for finding invariant sets of continuous systems. Zbl 1471.37018
Fribourg, Laurent; Goubault, Eric; Mohamed, Sameh; Mrozek, Marian; Putot, Sylvie
2015
Discrete Morse theoretic algorithms for computing homology of complexes and maps. Zbl 1387.55010
Harker, Shaun; Mischaikow, Konstantin; Mrozek, Marian; Nanda, Vidit
2014
CAPD::RedHom v2 – homology software based on reduction algorithms. Zbl 1402.57021
Juda, Mateusz; Mrozek, Marian
2014
The cubical cohomology ring: an algorithmic approach. Zbl 1350.55002
Kaczynski, Tomasz; Mrozek, Marian
2013
Distributed computation of coverage in sensor networks by homological methods. Zbl 1300.55001
Dłotko, P.; Ghrist, R.; Juda, M.; Mrozek, M.
2012
Topological dynamics: rigorous numerics via cubical homology. Zbl 1269.37019
Mrozek, Marian
2012
Homology computations via acyclic subspace. Zbl 1357.68260
Brendel, Piotr; Dłotko, Paweł; Mrozek, Marian; Żelazna, Natalia
2012
$$\mathbb{Z}_2$$-homology of weak $$(p-2)$$-faceless $$p$$-pseudomanifolds may be computed in $$O(n)$$ time. Zbl 1276.55003
Juda, Mateusz; Mrozek, Marian
2012
Coreduction homology algorithm for regular CW-complexes. Zbl 1229.55001
Dłotko, Paweł; Kaczynski, Tomasz; Mrozek, Marian; Wanner, Thomas
2011
Coreduction homology algorithm for inclusions and persistent homology. Zbl 1207.57001
Mrozek, Marian; Wanner, Thomas
2010
Topological approach to rigorous numerics of chaotic dynamical systems with strong expansion of error bounds. Zbl 1192.65152
Mrozek, Marian; Srzednicki, Roman
2010
Čech type approach to computing homology of maps. Zbl 1219.55004
Mrozek, Marian
2010
Homology of representable sets. Zbl 1198.68285
Mrozek, Marian; Batko, Bogdan
2010
Coreduction homology algorithm. Zbl 1163.68041
Mrozek, Marian; Batko, Bogdan
2009
Conley index of Poincaré maps in isolating segments. Zbl 1154.37315
Mrozek, Marian; Srzednicki, Roman
2009
Homology algorithm based on acyclic subspace. Zbl 1142.15300
Mrozek, Marian; Pilarczyk, Paweł; Ẓelazna, Natalia
2008
The Euler-Poincaré characteristic of index maps. Zbl 1108.37009
Batko, Bogdan; Mrozek, Marian
2007
Index pairs algorithms. Zbl 1111.37006
Mrozek, Marian
2006
The method of topological sections in the rigorous numerics of dynamical systems. Zbl 1136.37363
Mrozek, Marian
2006
Graph approach to the computation of the homology of continuous maps. Zbl 1104.55001
Mischaikow, Konstantin; Mrozek, Marian; Pilarczyk, Pawel
2005
Discrete version of a geometric method for detecting chaotic dynamics. Zbl 1078.37011
Mrozek, Marian; Wójcik, Klaudiusz
2005
Computational homology. Zbl 1039.55001
Kaczynski, Tomasz; Mischaikow, Konstantin; Mrozek, Marian
2004
Computing homology. Zbl 1028.55001
Kaczynski, Tomasz; Mischaikow, Konstantin; Mrozek, Marian
2003
Conley index. Zbl 1035.37010
Mischaikow, Konstantin; Mrozek, Marian
2002
The Conley index and rigorous numerics for attracting periodic orbits. Zbl 1040.37012
Mrozek, M.; Pilarczyk, P.
2002
Chaos in the Lorenz equations: A computer assisted proof. III: Classical parameter values. Zbl 0979.37015
Mischaikow, Konstantin; Mrozek, Marian; Szymczak, Andrzej
2001
Set arithmetic and the enclosing problem in dynamics. Zbl 0967.65113
Mrozek, Marian; Zgliczyński, Piotr
2000
The Conley index over a base. Zbl 0967.37011
Mrozek, Marian; Reineck, James F.; Srzednicki, Roman
2000
The Conley index over the circle. Zbl 0967.37010
Mrozek, Marian; Reineck, James F.; Srzednicki, Roman
2000
An algorithmic approach to the Conley index theory. Zbl 0941.37004
Mrozek, Marian
1999
Singular index pairs. Zbl 0943.34028
Mischaikow, Konstantin; Mrozek, Marian; Reineck, James F.
1999
Conley index theory. Zbl 0913.00021
1999
Chaos in the Lorenz equations: A computer assisted proof. II: Details. Zbl 0913.58038
Mischaikow, Konstantin; Mrozek, Marian
1998
Homology computation by reduction of chain complexes. Zbl 0904.55004
Kaczýnski, T.; Mrozek, M.; Ślusarek, M.
1998
Heteroclinic connections in the Kuramoto-Sivashinsky equation: A computer assisted proof. Zbl 0888.65091
Mrozek, Marian; Żelawski, Marcin
1997
Stable index pairs for discrete dynamical systems. Zbl 0903.54018
Kaczynski, Tomasz; Mrozek, Marian
1997
Connected simple systems and the Conley functor. Zbl 0909.54033
Kaczyński, Tomasz; Mrozek, Marian
1997
Topological invariants, multivalued maps and computer assisted proofs in dynamics. Zbl 0861.58027
Mrozek, Marian
1996
The Conley index and rigorous numerics. Zbl 0887.58036
Mrozek, M.
1996
Rigorous error analysis of numerical algorithms via symbolic computations. Zbl 0871.65035
Mrozek, Marian
1996
Inheritable properties and computer assisted proofs in dynamics. Zbl 0848.68102
Mrozek, Marian
1996
Chaos in the Lorenz equations: A computer-assisted proof. Zbl 0820.58042
Mischaikow, Konstantin; Mrozek, Marian
1995
Isolating neighborhoods and chaos. Zbl 0840.58033
Mischaikow, Konstantin; Mrozek, Marian
1995
Conley index for discrete multi-valued dynamical systems. Zbl 0843.54042
Kaczynski, T.; Mrozek, Marian
1995
Zeta functions, periodic trajectories, and the Conley index. Zbl 0833.34045
McCord, Christopher; Mischaikow, Konstantin; Mrozek, Marian
1995
From the theorem of Ważewski to computer assisted proofs in dynamics. Zbl 0848.34032
Mrozek, Marian
1995
Rigorous numerics of chaotic dynamical systems. Zbl 0840.65067
Mrozek, Marian
1995
Shape index and other indices of Conley type for local maps on locally compact Hausdorff spaces. Zbl 0870.54043
Mrozek, Marian
1994
On time-duality of the Conley index. Zbl 0783.34039
Mrozek, Marian; Srzednicki, Roman
1993
The Conley index for maps in absence of compactness. Zbl 0789.58066
Degiovanni, Marco; Mrozek, Marian
1993
Discretized ordinary differential equations and the Conley index. Zbl 0745.34041
Mrozek, Marian; Rybakowski, Krzysztof P.
1992
Normal functors and retractors in categories of endomorphisms. Zbl 0758.18004
Mrozek, Marian
1992
A cohomological Conley index for maps on metric spaces. Zbl 0721.58040
Mrozek, Marian; Rybakowski, Krzysztof P.
1991
The Morse equation in Conley’s index theory for homeomorphisms. Zbl 0725.58022
Mrozek, Marian
1991
Nontrivial full bounded solutions of time-periodic semilinear parabolic PDEs. Zbl 0739.35030
Mrozek, Marian; Rybakowski, Krzysztof P.
1991
Some remarks on Garay’s conjecture. Zbl 0749.54007
Mrozek, M.
1991
Leray functor and cohomological Conley index for discrete dynamical systems. Zbl 0686.58034
Mrozek, Marian
1990
A cohomological index of Conley type for multi-valued admissible flows. Zbl 0703.34019
Mrozek, Marian
1990
The Conley index on compact ANR’s is of finite type. Zbl 0723.54038
Mrozek, Marian
1990
Open index pairs, the fixed point index and rationality of zeta functions. Zbl 0696.58044
Mrozek, Marian
1990
Index pairs and the fixed point index for semidynamical systems with discrete time. Zbl 0708.58024
Mrozek, Marian
1989
Periodic and stationary trajectories of flows and ordinary differential equations. Zbl 0684.34046
Mrozek, Marian
1988
The fixed point index of a translation operator of a semiflow. Zbl 0674.54027
Mrozek, Marian
1988
The continuity axiom in multi-valued dynamical systems. Zbl 0689.54024
Mrozek, Marian; Srzednicki, Roman
1988
all top 5

### Cited by 561 Authors

 47 Mrozek, Marian 29 Mischaikow, Konstantin 17 Zgliczyński, Piotr 12 Pilarczyk, Paweł 11 Kaczynski, Tomasz 11 Wanner, Thomas 10 Srzednicki, Roman 10 Wójcik, Klaudiusz 9 Ruiz del Portal, Francisco Romero 8 Ghrist, Robert W. 8 Hiraoka, Yasuaki 8 Kalies, William D. 8 Kokubu, Hiroshi 8 Li, Desheng 7 Allili, Madjid 7 Dłotko, Paweł 7 Gedeon, Tomáš 7 Mireles-James, Jason D. 7 Wilczak, Daniel 6 Batko, Bogdan 6 Day, Sarah L. 6 Gabor, Grzegorz 6 Harker, Shaun 6 Juda, Mateusz 6 Nanda, Vidit 6 Romero, Ana 6 Sanjurjo, José M. R. 6 Yang, Xiaosong 5 Ellis, Graham J. 5 Galias, Zbigniew 5 Gameiro, Marcio F. 5 González-Díaz, Rocío 5 Landi, Claudia 5 Lessard, Jean-Philippe 5 Moron, Manuel Alonso 5 Real, Pedro 5 Rybakowski, Krzysztof P. 5 Vandervorst, Robertus C. A. M. 5 Wiseman, Jim 5 Zanolin, Fabio 4 Barge Yáñez, Héctor 4 Capinski, Maciej J. 4 Dzedzej, Zdzisław 4 Lienhardt, Pascal 4 Peltier, Samuel 4 Pireddu, Marina 4 Szymczak, Andrzej 4 Wei, Guowei 3 Arai, Zin 3 Bauer, Ulrich 3 Bielecki, Andrzej 3 Bradley, Elizabeth 3 Collins, Peter J. 3 Duan, Jinqiao 3 Edelsbrunner, Herbert 3 Garay, Barnabas M. 3 Gidea, Marian 3 Giraldo, Antonio 3 Goubault, Eric 3 Guidolin, Andrea 3 Hernández-Corbato, Luis 3 Jablonski, Grzegorz 3 Kapela, Tomasz 3 Kramár, Miroslav 3 Li, Chunqiu 3 Meiss, James D. 3 Obayashi, Ippei 3 Oka, Hiroe 3 Richeson, David S. 3 Specogna, Ruben 3 Tucker, Warwick 3 van den Berg, Jan Bouwe 3 Wang, Jintao 3 Weilandt, Frank 2 Alayrangues, Sylvie 2 Andres, Jan 2 Bac, Alexandra 2 Bánhelyi, Balázs 2 Barabash, Nikita V. 2 Barrio, Roberto 2 Belykh, Igor V. 2 Belykh, Vladimir Nikitich 2 Boscaggin, Alberto 2 Bush, Justin 2 Carbinatto, Maria C. 2 Cerri, Andrea 2 Chen, Jiahui 2 Chung, Yu-Min 2 Corriveau, David 2 Damiand, Guillaume 2 de Rezende, Ketty Abaroa 2 de Silva, Vin 2 DeFloriani, Leila 2 Dey, Tamal Krishna 2 di Fabio, Barbara 2 Dubut, Jérémy 2 Ege, Ozgur 2 Ethier, Marc 2 Ferri, Massimo 2 Franzosa, Robert D. ...and 461 more Authors
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### Cited in 130 Serials

 38 Journal of Differential Equations 25 Topology and its Applications 18 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 18 SIAM Journal on Applied Dynamical Systems 17 Discrete & Computational Geometry 16 Foundations of Computational Mathematics 15 Journal of Dynamics and Differential Equations 14 Physica D 13 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Journal of Applied and Computational Topology 9 Chaos, Solitons and Fractals 9 Transactions of the American Mathematical Society 9 Communications in Nonlinear Science and Numerical Simulation 7 Journal of Symbolic Computation 6 Computers & Mathematics with Applications 6 Applicable Algebra in Engineering, Communication and Computing 6 Chaos 5 Proceedings of the American Mathematical Society 5 Computational Geometry 5 Discrete and Continuous Dynamical Systems 4 Journal of Mathematical Analysis and Applications 4 Mathematics of Computation 4 Ergodic Theory and Dynamical Systems 4 Japan Journal of Industrial and Applied Mathematics 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Topological Methods in Nonlinear Analysis 4 Journal of Difference Equations and Applications 4 Nonlinear Analysis. Theory, Methods & Applications 3 Applied Mathematics and Computation 3 Journal of Computational and Applied Mathematics 3 Applied Numerical Mathematics 3 Journal of Mathematical Imaging and Vision 3 Advances in Computational Mathematics 3 Nonlinear Analysis. Real World Applications 3 Journal of Computational Dynamics 2 Computer Methods in Applied Mechanics and Engineering 2 Rocky Mountain Journal of Mathematics 2 Mathematics and Computers in Simulation 2 Mathematische Zeitschrift 2 Theoretical Computer Science 2 Computer Aided Geometric Design 2 The Annals of Applied Probability 2 Pattern Recognition 2 Bulletin of the American Mathematical Society. New Series 2 Applied Categorical Structures 2 Annals of Mathematics and Artificial Intelligence 2 Revista Matemática Complutense 2 Differential Equations 2 Algebraic & Geometric Topology 2 Discrete and Continuous Dynamical Systems. Series B 2 Journal of Fixed Point Theory and Applications 2 SIAM Journal on Applied Algebra and Geometry 1 Computer Physics Communications 1 Communications on Pure and Applied Mathematics 1 Discrete Applied Mathematics 1 International Journal of Theoretical Physics 1 Journal of Computational Physics 1 Journal of Mathematical Biology 1 Journal of Statistical Physics 1 Mathematical Methods in the Applied Sciences 1 Bulletin of Mathematical Biology 1 The Mathematical Intelligencer 1 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Statistics 1 BIT 1 Collectanea Mathematica 1 Duke Mathematical Journal 1 Fuzzy Sets and Systems 1 Geometriae Dedicata 1 Glasgow Mathematical Journal 1 Journal of Algebra 1 Journal of Computer and System Sciences 1 Journal of Pure and Applied Algebra 1 Kybernetika 1 Monatshefte für Mathematik 1 Numerical Functional Analysis and Optimization 1 Results in Mathematics 1 Zeitschrift für Analysis und ihre Anwendungen 1 ACM Transactions on Graphics 1 Information and Computation 1 Journal of the American Mathematical Society 1 Dynamics and Stability of Systems 1 Science in China. Series A 1 International Journal of Mathematics 1 Glasnik Matematički. Serija III 1 Linear Algebra and its Applications 1 Proceedings of the National Academy of Sciences of the United States of America 1 Indagationes Mathematicae. New Series 1 Journal of Knot Theory and its Ramifications 1 Journal of Nonlinear Science 1 Experimental Mathematics 1 Set-Valued Analysis 1 Communications in Numerical Methods in Engineering 1 International Journal of Computer Vision 1 Filomat 1 Electronic Research Announcements of the American Mathematical Society 1 Abstract and Applied Analysis 1 Geometry & Topology 1 Journal of Shanghai University ...and 30 more Serials
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### Cited in 45 Fields

 246 Dynamical systems and ergodic theory (37-XX) 112 Algebraic topology (55-XX) 86 Ordinary differential equations (34-XX) 70 Computer science (68-XX) 69 Numerical analysis (65-XX) 51 General topology (54-XX) 33 Manifolds and cell complexes (57-XX) 28 Partial differential equations (35-XX) 24 Biology and other natural sciences (92-XX) 19 Combinatorics (05-XX) 16 Statistics (62-XX) 15 Global analysis, analysis on manifolds (58-XX) 15 Probability theory and stochastic processes (60-XX) 14 Category theory; homological algebra (18-XX) 10 Operator theory (47-XX) 10 Information and communication theory, circuits (94-XX) 9 Order, lattices, ordered algebraic structures (06-XX) 8 Convex and discrete geometry (52-XX) 8 Systems theory; control (93-XX) 7 Mechanics of particles and systems (70-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Algebraic geometry (14-XX) 5 Mathematical logic and foundations (03-XX) 5 Fluid mechanics (76-XX) 5 Operations research, mathematical programming (90-XX) 4 Difference and functional equations (39-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Differential geometry (53-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 History and biography (01-XX) 2 Associative rings and algebras (16-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Mechanics of deformable solids (74-XX) 2 Optics, electromagnetic theory (78-XX) 2 Geophysics (86-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Quantum theory (81-XX)