Linking combinatorial and classical dynamics: Conley index and Morse decompositions

DOI10.1007/s10208-020-09444-1zbMath1456.37040arXiv1710.05802OpenAlexW3100133068WikidataQ126304211 ScholiaQ126304211MaRDI QIDQ2216246

Thomas Wanner, Marian Mrozek, Tomasz Kaczynski, Bogdan Batko

Publication date: 15 December 2020

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.05802

zbMATH Keywords

simplicial complexisolated invariant setMorse decompositionisolating blockdiscrete Morse theorycombinatorial vector fieldConley theorymultivalued dynamical systemConley-Morse graph

Mathematics Subject Classification ID

General topology of complexes (57Q05) Triangulating manifolds (57Q15) Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems (37B35) Index theory for dynamical systems, Morse-Conley indices (37B30) Combinatorial dynamics (types of periodic orbits) (37E15)

Related Items (8)

Discrete stratified Morse theory. Algorithms and a user's guide ⋮ Persistence of Morse decompositions over grid resolution for maps and time series ⋮ Persistence of Conley--Morse Graphs in Combinatorial Dynamical Systems ⋮ The Morse equation in the Conley index theory for discrete multivalued dynamical systems ⋮ Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces ⋮ 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

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• Towards a formal tie between combinatorial and classical vector field dynamics
• Morse theory for filtrations and efficient computation of persistent homology
• Discrete Morse theoretic algorithms for computing homology of complexes and maps
• On homotopy Conley index for multivalued flows in Hilbert spaces
• The Conley index on compact ANR's is of finite type
• Homotopy Conley index for discrete multivalued dynamical systems
• A cohomological index of Conley type for multi-valued admissible flows
• Conley type index applied to Hamiltonian inclusions
• An addendum to the Vietoris-Begle theorem
• Combinatorial vector fields and dynamical systems
• Morse theory for cell complexes
• Conley-Morse-Forman theory for combinatorial multivector fields on Lefschetz complexes
• Topological invariants, multivalued maps and computer assisted proofs in dynamics
• Conley index for discrete multi-valued dynamical systems
• The Conley index for discrete semidynamical systems
• On generalized dynamical systems defined by contingent equations
• Singular homology groups and homotopy groups of finite topological spaces
• Stability in general control systems
• Discrete Morse theory and graph braid groups.
• Combinatorial-topological framework for the analysis of global dynamics
• The Morse theory of Čech and Delaunay complexes
• Weak Index Pairs and the Conley Index for Discrete Multivalued Dynamical Systems
• Leray Functor and Cohomological Conley Index for Discrete Dynamical Systems
• Chaos in the Lorenz equations: a computer-assisted proof
• Weak Index Pairs and the Conley Index for Discrete Multivalued Dynamical Systems. Part II: Properties of the Index
• A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems
• Topological Fixed Point Theory of Multivalued Mappings
• Fitting ordinary differential equations to short time course data

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