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Combinatorial vector fields and dynamical systems

https://doi.org/10.1007/pl00004638
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Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1006/aima.1997.1650openalex-snapshot
Morse Theory for Cell Complexes
inferredcites →https://doi.org/10.1007/978-1-4684-6254-8openalex-snapshot
The Topology of CW Complexes
inferredcites →https://doi.org/10.1007/bf02772984openalex-snapshot
A combinatorial decomposition of simplicial complexes
inferredcites →https://doi.org/10.1016/0001-8708(71)90045-4openalex-snapshot
R-Torsion and the Laplacian on Riemannian manifolds
inferredcites →https://doi.org/10.1016/0012-365x(93)90574-dopenalex-snapshot
A combinatorial decomposition of acyclic simplicial complexes
inferredcites →https://doi.org/10.1016/0040-9383(93)90035-topenalex-snapshot
Determinants of Laplacians on graphs
inferredcites →https://doi.org/10.1090/cbms/038openalex-snapshot
Isolated Invariant Sets and the Morse Index
inferredcites →https://doi.org/10.1090/cbms/049openalex-snapshot
Homology and Dynamical Systems
inferredcites →https://doi.org/10.1515/crll.1935.173.245openalex-snapshot
Über die Torsion einer Überdeckung.

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Morse Theory for Cell Complexes
inferred← citeshttps://doi.org/10.1007/978-1-4939-2149-2_1openalex-snapshot
Background
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Combinatorial Control Systems
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Introduction to Vector Field Topology
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Topological Foundations, Hypercomplexes and Homology
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Connection Matrices in Combinatorial Topological Dynamics
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Dynamics of Combinatorial Multivector Fields
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Connection Matrices for Gradient Vector Fields
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Simplification of Morse Decompositions Using Morse Set Mergers
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Homological Shape Analysis Through Discrete Morse Theory
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Sliding Algorithm for Reconfigurable Arrays of Processors
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Combinatorial 2D Vector Field Topology Extraction and Simplification
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TADD: A Computational Framework for Data Analysis Using Discrete Morse Theory
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Smale-Like Decomposition and Forman Theory for Discrete Scalar Fields
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Computational Discrete Morse Theory for Divergence-Free 2D Vector Fields
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Combinatorial Vector Field Topology in Three Dimensions
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Geometry and Coarse-Grained Representations of Landscapes
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Searching combinatorial optimality using graph-based homology information
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A Lefschetz fixed point theorem for multivalued maps of finite spaces
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Combinatorial vector fields and the valley structure of fitness landscapes
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Morse Theory and Evasiveness
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Characterizing equivalent discrete Morse functions
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Conley–Morse–Forman Theory for Combinatorial Multivector Fields on Lefschetz Complexes
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Linking Combinatorial and Classical Dynamics: Conley Index and Morse Decompositions
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Conley Index for Multivalued Maps on Finite Topological Spaces
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Morse Predecomposition of an Invariant Set
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From numerics to combinatorics: a survey of topological methods for vector field visualization
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Morse–Bott inequalities for endomorphisms
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A Generalized Discrete Morse–Floer Theory
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Floer Homology: From Generalized Morse–Smale Dynamical Systems to Forman’s Combinatorial Vector Fields
inferred← citeshttps://doi.org/10.1007/s41468-022-00102-9openalex-snapshot
Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces
inferred← citeshttps://doi.org/10.1007/s41468-024-00181-wopenalex-snapshot
From finite vector field data to combinatorial dynamical systems in the sense of Forman
inferred← citeshttps://doi.org/10.1016/b978-1-68108-053-6.50013-2openalex-snapshot
Generalized Topologies: Hypergraphs, Chemical Reactions, and Biological Evolution
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Computing a discrete Morse gradient from a watershed decomposition
inferred← citeshttps://doi.org/10.1016/j.cagd.2012.03.022openalex-snapshot
Morse connection graphs for piecewise constant vector fields on surfaces
inferred← citeshttps://doi.org/10.1016/j.jde.2021.10.001openalex-snapshot
Creating semiflows on simplicial complexes from combinatorial vector fields
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Integration of vector fields on cell complexes and Morse theory
inferred← citeshttps://doi.org/10.1016/j.topol.2007.04.023openalex-snapshot
A note on the pure Morse complex of a graph
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Allowing cycles in discrete Morse theory
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Discrete line fields on surfaces
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MORSE INEQUALITIES ON CERTAIN INFINITE 2-COMPLEXES
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Topics in combinatorial differential topology and geometry
inferred← citeshttps://doi.org/10.1090/s0002-9947-02-03041-6openalex-snapshot
Discrete morse theory and the cohomology ring
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Combinatorial hybrid systems
inferred← citeshttps://doi.org/10.1109/tvcg.2010.235openalex-snapshot
Fast Combinatorial Vector Field Topology
inferred← citeshttps://doi.org/10.1109/tvcg.2011.107openalex-snapshot
Morse Set Classification and Hierarchical Refinement Using Conley Index
inferred← citeshttps://doi.org/10.1109/tvcg.2011.269openalex-snapshot
Efficient Computation of Combinatorial Feature Flow Fields
inferred← citeshttps://doi.org/10.1109/tvcg.2011.88openalex-snapshot
Robust Morse Decompositions of Piecewise Constant Vector Fields
inferred← citeshttps://doi.org/10.1109/tvcg.2012.147openalex-snapshot
Hierarchy of Stable Morse Decompositions
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Visualization of Morse Connection Graphs for Topologically Rich 2D Vector Fields
inferred← citeshttps://doi.org/10.1109/tvcg.2024.3456355openalex-snapshot
Localized Evaluation for Constructing Discrete Vector Fields
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Morse complexes for shape segmentation and homological analysis: discrete models and algorithms
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Visualization of Tensor Fields in Mechanics
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Topology‐based Visual Analysis of Hydrothermal Plumes
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The persistent cosmic web and its filamentary structure - I. Theory and implementation
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Stable Morse Decompositions for Piecewise Constant Vector Fields on Surfaces
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A Quantized Boundary Representation of 2D Flows
inferred← citeshttps://doi.org/10.1111/j.1467-8659.2012.03104.xopenalex-snapshot
Nearly Recurrent Components in 3D Piecewise Constant Vector Fields
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Weak Index Pairs and the Conley Index for Discrete Multivalued Dynamical Systems
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Weak Index Pairs and the Conley Index for Discrete Multivalued Dynamical Systems. Part II: Properties of the Index
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Persistent Homology of Morse Decompositions in Combinatorial Dynamics
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Unsupervised Features Learning for Sampled Vector Fields
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Persistence of Conley--Morse Graphs in Combinatorial Dynamical Systems
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Computing Connection Matrices via Persistence-Like Reductions
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Tagged Barcodes for the Topological Analysis of Gradient-Like Vector Fields
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COMBINATORIAL NOVIKOV–MORSE THEORY
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Morse–Bott theory on posets and a homological Lusternik–Schnirelmann theorem
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DISCRETE LINE FIELDS ON SURFACES
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ConleyDynamics.jl: A Julia package for multivector dynamics on Lefschetz complexes
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Consistent Feature Extraction From Vector Fields: Combinatorial Representations and Analysis Under Local Reference Frames
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Combinatorial realization of the Thom-Smale complex via discrete Morse theory
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NASA CFD Vision 2030 Visualization and Knowledge Extraction: Panel Summary from AIAA AVIATION 2015 Conference
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Combinatorial Ricci curvature on cell-complex and Gauss-Bonnnet theorem
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A combinatorial perspective on shape theory
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Combinatorial Vector Fields for Piecewise Affine Control Systems
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Characteristically Near Stable Vector Fields in the Polar Complex Plane
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Optimization of Encoding Design Based on the Spatial Geometry Remarkable Properties
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Big Data Process Engineering under Manifold Coordinate Systems
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Discrete gradient fields on infinite complexes
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Towards a formal tie between combinatorial and classical vector field dynamics
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Persistence of the Conley Index in Combinatorial Dynamical Systems
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The Combinatorial Norm of a Morphism of Schemes
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Lefschetz Complexes as Finite Topological Spaces
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Dynamical systems on chain complexes and canonical minimal resolutions
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Poincare Hopf for vector fields on graphs
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Morse-Bott Theory on posets and an homological Lusternik-Schnirelmann Theorem
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Coincidence theorems for finite topological spaces
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Morse theory for loop-free categories
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On The Discrete Morse Functions for Hypergraphs
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Characteristically Near Stable Vector Fields in the Polar Complex Plane
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Figure 16 In A Description Of Two New Species Of The Genus Erenna (Siphonophora: Physonectae: Erennidae), With Notes On Recently Collected Specimens Of Other Erenna Species
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Matching Cells
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Optimisation de la couverture de communication et de mesure dans les réseaux de capteurs
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Computational homology applied to discrete objects
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