Takens-type reconstruction theorems of one-sided dynamical systems

DOI10.1088/1361-6544/acb396OpenAlexW4318778254WikidataQ121792896 ScholiaQ121792896MaRDI QIDQ5875958

Hisao Kato

Publication date: 7 February 2023

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.01482

zbMATH Keywords

fractal setstopological dimensiontime-delay embeddingbranched manifoldsone-sided topological dynamical systemsTakens' reconstruction theorem

Mathematics Subject Classification ID

Topological spaces of dimension (leq 1); curves, dendrites (54F50) Dimension theory in general topology (54F45) Embedding (54C25) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Geometric embeddings of metric spaces (30L05) Dynamics in general topological spaces (37B02)

Cites Work

• Chain recurrent sets of generic mappings on compact spaces
• Observability and topological dynamics
• Embedology
• The reconstruction theorem for endomorphisms
• Mean dimension, small entropy factors and an embedding theorem
• Mean topological dimension
• Finite-to-one zero-dimensional covers of dynamical systems
• Topological dimension and dynamical systems. Translated from the French by the author
• Mean dimension and a sharp embedding theorem: extensions of aperiodic subshifts
• Takens' embedding theorem with a continuous observable
• Topological characterization of the Sierpiński curve
• Mean dimension and Jaworski-type theorems
• The chain recurrent set, attractors, and explosions
• THE TAKENS EMBEDDING THEOREM
• The embedding problem in topological dynamics and Takens’ theorem
• Observing expansive maps
• The Topology of Chaos
• Jaworski-type embedding theorems of one-sided dynamical systems
• Characterizing 𝑘-dimensional universal Menger compacta
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