Persistent Homology of Morse Decompositions in Combinatorial Dynamics

DOI10.1137/18M1198946zbMath1415.37058arXiv1801.06590OpenAlexW2964330932WikidataQ128251643 ScholiaQ128251643MaRDI QIDQ5383198

Michał Lipiński, Tomasz Kapela, Marian Mrozek, Jacek Kubica, Tamal Krishna Dey, Mateusz Juda

Publication date: 20 June 2019

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.06590

zbMATH Keywords

time seriesMorse decompositiondiscrete vector fieldsampled dynamicshomological persistence

Mathematics Subject Classification ID

Time series analysis of dynamical systems (37M10) Combinatorial dynamics (types of periodic orbits) (37E15) Other homology theories in algebraic topology (55N35)

Related Items

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 ⋮ On the dynamics of the combinatorial model of the real line ⋮ Computing Connection Matrices via Persistence-Like Reductions ⋮ Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces ⋮ Spatiotemporal persistent homology for dynamic metric spaces ⋮ Creating semiflows on simplicial complexes from combinatorial vector fields ⋮ Conley Index Approach to Sampled Dynamics ⋮ A Lefschetz fixed point theorem for multivalued maps of finite spaces ⋮ Unsupervised Features Learning for Sampled Vector Fields

Cites Work

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• Architecture of attractor determines dynamics on mutualistic complex networks
• Morse decompositions with infinite components for multivalued semiflows
• The persistent homology of a self-map
• Combinatorial vector fields and dynamical systems
• Morse theory for cell complexes
• Conley-Morse-Forman theory for combinatorial multivector fields on Lefschetz complexes
• Modeling complex systems
• Topological persistence and simplification
• Zigzag persistence
• Algebraic topology of finite topological spaces and applications
• Skew product semiflows and Morse decomposition
• Singular homology groups and homotopy groups of finite topological spaces
• Combinatorial-topological framework for the analysis of global dynamics
• Topology and data
• Chaos in the Lorenz equations: a computer-assisted proof
• Computing Topological Persistence for Simplicial Maps
• A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems
• Rich Bifurcation Structure in a Two-Patch Vaccination Model
• Simplicial Multivalued Maps and the Witness Complex for Dynamical Analysis of Time Series
• Zigzag persistent homology and real-valued functions
• On Morse decompositions of control systems
• Elements of applied bifurcation theory
• Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces