Towards a formal tie between combinatorial and classical vector field dynamics

DOI10.3934/jcd.2016002zbMath1353.37096OpenAlexW2519753363MaRDI QIDQ333772

Tomasz Kaczynski, Marian Mrozek, Thomas Wanner

Publication date: 31 October 2016

Published in: Journal of Computational Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jcd.2016002

zbMATH Keywords

simplicial complexmultivalued mapsisolated invariant setdiscrete dynamical systemdiscrete Morse theorycombinatorial vector fieldConley theory

Mathematics Subject Classification ID

General topology of complexes (57Q05) Combinatorial dynamics (types of periodic orbits) (37E15) Combinatorics and topology in relation with holomorphic dynamical systems (37F20)

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Persistence of Conley--Morse Graphs in Combinatorial Dynamical Systems, Lattice structures for attractors. III, Weak Index Pairs and the Conley Index for Discrete Multivalued Dynamical Systems. Part II: Properties of the Index, Conley-Morse-Forman theory for combinatorial multivector fields on Lefschetz complexes, Computing Connection Matrices via Persistence-Like Reductions, Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces, Linking combinatorial and classical dynamics: Conley index and Morse decompositions, Creating semiflows on simplicial complexes from combinatorial vector fields, A Lefschetz fixed point theorem for multivalued maps of finite spaces, Combinatorial vs. classical dynamics: recurrence

Cites Work

• Unnamed Item
• Coreduction homology algorithm
• Combinatorial vector fields and dynamical systems
• Morse theory for cell complexes
• Computational homology
• Conley index for discrete multi-valued dynamical systems
• Rigorous Validation of Isolating Blocks for Flows and Their Conley Indices
• Weak Index Pairs and the Conley Index for Discrete Multivalued Dynamical Systems
• Generating Discrete Morse Functions from Point Data
• An algorithmic approach to the construction of homomorphisms induced by maps in homology
• Topological Fixed Point Theory of Multivalued Mappings
• Isolated Invariant Sets and Isolating Blocks