Exploring the topology of dynamical reconstructions

DOI10.1016/j.physd.2016.03.006zbMath1415.37103arXiv1506.01128OpenAlexW2267136012MaRDI QIDQ1999934

Elizabeth Bradley, Joshua Garland, James D. Meiss

Publication date: 27 June 2019

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.01128

zbMATH Keywords

topologynonlinear time series analysiscomputational homologywitness complexdelay-coordinate embedding

Mathematics Subject Classification ID

Time series analysis of dynamical systems (37M10) Simplicial sets and complexes in algebraic topology (55U10)

Related Items (12)

Persistence of Morse decompositions over grid resolution for maps and time series ⋮ Persistent topological features of dynamical systems ⋮ Inferring symbolic dynamics of chaotic flows from persistence ⋮ Fractal dimension estimation with persistent homology: a comparative study ⋮ Topological data analysis for true step detection in periodic piecewise constant signals ⋮ Geometric Metrics for Topological Representations ⋮ Embedding and approximation theorems for echo state networks ⋮ Topological characterization and early detection of bifurcations and chaos in complex systems using persistent homology ⋮ Editorial: Topology in dynamics, differential equations, and data ⋮ A chaos theoretic approach to animal activity recognition ⋮ Chaoticity versus stochasticity in financial markets: are daily S\&P 500 return dynamics chaotic? ⋮ Topology of dynamical reconstructions from Lagrangian data

Cites Work

• Unnamed Item
• The structure of Lorenz attractors
• State space reconstruction in the presence of noise
• Embedology
• Computational homology
• Computing persistent homology
• Zigzag persistence
• Finding the homology of submanifolds with high confidence from random samples
• Homology groups of relations
• Iterated function system models in data analysis: Detection and separation
• Computing multidimensional persistence
• Independent coordinates for strange attractors from mutual information
• Alpha-Beta Witness Complexes
• Nonlinear time-series analysis revisited
• Deterministic Nonperiodic Flow
• Topological pattern recognition for point cloud data
• Automatic Recognition and Tagging of Topologically Different Regimes in Dynamical Systems
• Simplicial Multivalued Maps and the Witness Complex for Dynamical Analysis of Time Series
• Barcodes: The persistent topology of data

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