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Algorithmic Computation of the Conley Index for Multivalued Maps with No Continuous Selector in Cubical Spaces

Publication date: 2019

Schedae Informaticae, 2019, Volume 28, pp. 9 - 24

https://doi.org/10.4467/20838476SI.19.001.14284

Authors

Mateusz Przybylski
Faculty of Mathematics and Computer Science, Jagiellonian University, Krakow, Poland
https://orcid.org/0000-0002-3467-2396 Orcid
All publications →

Titles

Algorithmic Computation of the Conley Index for Multivalued Maps with No Continuous Selector in Cubical Spaces

Abstract

In this note we present theory which facilitates the use of Conley index algorithms for cubical multivalued maps constructed from maximal dimensional cubes in the setting when cubes of arbitrary dimension are permitted.

References

[1] Batko B.; Weak index pairs and the Conley index for discrete multivalued dynamical systems. Part II: properties of the Index, SIAM Journal on Applied Dynamical Systems, 16(3), 2017, pp. 1587–1617.

[2] Batko B., Mischaikow K., Mrozek M., Przybylski M.; Conley index approach to sampled dynamics, in review.

[3] Batko B., Mrozek M.; Weak index pairs and the Conley index for discrete multivalued dynamical systems, SIAM Journal on Applied Dynamical Systems, 15(2), 2016, pp. 1143–1162.

[4] G´orniewicz L.; Topological Fixed Point Theory of Multivalued Mappings, 2nd ed., Topological Fixed Point Theory and Its Applications, Vol. 4, Springer Verlag, The Netherlands, 2006.

[5] Kaczynski T., Mischaikow K., Mrozek M.; Computational Homology, Applied Mathematical Sciences, Vol. 157, Springer-Verlag, 2004.

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[7] Engelking R.; General Topology, Sigma series in pure mathematics, Vol. 6, Heldermann Verlag Berlin, 1989.

[8] Mischaikow K., Mrozek M., Pilarczyk P.; Graph approach to the computation of the homology of continuous maps, Foundations of Computational Mathematics, 5(2), 2005, pp. 199–229.

[9] Mrozek M.; Leray functor and cohomological index for discrete dynamical systems, Transactions of the American Mathematical Society, 318(1), 1990, pp. 149–178.

[10] Pilarczyk P.; CHomP software, 2005. Available via http://chomp.rutgers.edu/Projects/Computational_Homology/OriginalCHomP/software/.

[11] Sakai K.; Cell-Like Maps and Related Topics, in: Geometric Aspects of General Topology, Springer Monographs in Mathematics, Springer Tokyo, 2013.

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Information

Information: Schedae Informaticae, 2019, Volume 28, pp. 9 - 24

Article type: Original article

Titles:

Polish:

Algorithmic Computation of the Conley Index for Multivalued Maps with No Continuous Selector in Cubical Spaces

English:

Algorithmic Computation of the Conley Index for Multivalued Maps with No Continuous Selector in Cubical Spaces

Authors

https://orcid.org/0000-0002-3467-2396

Mateusz Przybylski
Faculty of Mathematics and Computer Science, Jagiellonian University, Krakow, Poland
https://orcid.org/0000-0002-3467-2396 Orcid
All publications →

Faculty of Mathematics and Computer Science, Jagiellonian University, Krakow, Poland

Published at: 2019

Article status: Open

Licence: CC BY-NC-ND  licence icon

Percentage share of authors:

Mateusz Przybylski (Author) - 100%

Article corrections:

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Publication languages:

English