Creating semiflows on simplicial complexes from combinatorial vector fields
From MaRDI portal
Publication:2235675
DOI10.1016/j.jde.2021.10.001OpenAlexW3206848412MaRDI QIDQ2235675
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
isolated invariant setMorse decompositiondiscrete Morse theorycombinatorial vector fieldConley theoryConley-Morse graph
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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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
