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

• Autorzy: Przybylski Mateusz

Identyfikatory

DOI

10.4467/20838476SI.19.001.14284

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

discrete multivalued dynamical system; cubical spaces; multivalued maps without continuous selector; Conley index; commutativity property

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Schedae Informaticae
• Rocznik: 2019
• Tom: Vol. 28
• Strony: 9--24
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Przybylski Mateusz

• Division of Computational Mathematics Faculty of Mathematics and Computer Science, Jagiellonian University Lojasiewicza 6, 30-348 Kraków, Poland

Bibliografia

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• [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] Górniewicz 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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• [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.
• [12] Szymczak A.; A combinatorial procedure for finding isolating neighborhoods and index pairs, Proceedings of the Royal Society of Edinburgh, A127(5), 1997, pp. 1075–1088.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).