Creating semiflows on simplicial complexes from combinatorial vector fields

DOI10.1016/j.jde.2021.10.001OpenAlexW3206848412MaRDI QIDQ2235675

Thomas Wanner, Marian Mrozek

Publication date: 21 October 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.11647

zbMATH Keywords

isolated invariant setMorse decompositiondiscrete Morse theorycombinatorial vector fieldConley theoryConley-Morse graph

Mathematics Subject Classification ID

General topology of complexes (57Q05) Dynamics induced by flows and semiflows (37C10) 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)

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Persistence of Conley--Morse Graphs in Combinatorial Dynamical Systems, On the dynamics of the combinatorial model of the real line, Integration of vector fields on cell complexes and Morse theory, Computing Connection Matrices via Persistence-Like Reductions, Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces, Combinatorial vs. classical dynamics: recurrence, Diffusion in multi-dimensional solids using Forman's combinatorial differential forms

Cites Work

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• Discretization strategies for computing Conley indices and Morse decompositions of flows
• 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
• The Vietoris mapping theorem for bicompact spaces. II
• Equivariant discrete Morse theory
• Vietoris-Begle theorem
• An addendum to the Vietoris-Begle theorem
• The homotopy index and partial differential equations
• Combinatorial vector fields and dynamical systems
• Witten-Morse theory for cell complexes
• Morse theory for cell complexes
• Bochner's method for cell complexes and combinatorial Ricci curvature
• A user's guide to discrete Morse theory
• Conley-Morse-Forman theory for combinatorial multivector fields on Lefschetz complexes
• A Vietoris-Begle theorem for connective Steenrod homology theories and cell-like maps between metric compacta
• Delay equations. Functional-, complex-, and nonlinear analysis
• Linking combinatorial and classical dynamics: Conley index and Morse decompositions
• Algebraic topology of finite topological spaces and applications
• A Lefschetz fixed point theorem for multivalued maps of finite spaces
• Piecewise-smooth dynamical systems. Theory and applications
• Singular homology groups and homotopy groups of finite topological spaces
• Regular cycles of compact metric spaces
• The Vietoris mapping theorem for bicompact spaces
• The Morse theory of Čech and Delaunay complexes
• Smale-Like Decomposition and Forman Theory for Discrete Scalar Fields
• Discrete morse theory and the cohomology ring
• Smoothing discrete Morse theory
• Minimal resolutions via algebraic discrete Morse theory
• Connected Simple Systems, Transition Matrices and Heteroclinic Bifurcations
• Homological Shape Analysis Through Discrete Morse Theory
• COMBINATORIAL NOVIKOV–MORSE THEORY
• Combinatorial realization of the Thom-Smale complex via discrete Morse theory
• Topological Computation Analysis of Meteorological Time-Series Data
• Morse Theory
• Simplicial Multivalued Maps and the Witness Complex for Dynamical Analysis of Time Series
• Persistent Homology of Morse Decompositions in Combinatorial Dynamics
• Using the Borsuk-Ulam theorem. Lectures on topological methods in combinatorics and geometry. Written in cooperation with Anders Björner and Günter M. Ziegler