Persistent Homology of Morse Decompositions in Combinatorial Dynamics
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Publication:5383198
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
Time series analysis of dynamical systems (37M10) Combinatorial dynamics (types of periodic orbits) (37E15) Other homology theories in algebraic topology (55N35)
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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