Excision-preserving cubical approach to the algorithmic computation of the discrete Conley index

DOI10.1016/j.topol.2008.02.003zbMath1149.37010OpenAlexW2013551157WikidataQ112163852 ScholiaQ112163852MaRDI QIDQ930001

Paweł Pilarczyk, Kinga Stolot

Publication date: 19 June 2008

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2008.02.003

zbMATH Keywords

Conley indexcomputational homologyindex pair

Mathematics Subject Classification ID

Index theory for dynamical systems, Morse-Conley indices (37B30) Approximation methods and numerical treatment of dynamical systems (37M99)

Related Items

Global dynamics in a stage-structured discrete-time population model with harvesting, A study of rigorous ODE integrators for multi-scale set-oriented computations, Recent development in rigorous computational methods in dynamical systems, Homotopy Conley index for discrete multivalued dynamical systems, An absorbing set for the Chialvo map, Excision-preserving cubical approach to the algorithmic computation of the discrete Conley index, Finite resolution dynamics, Computation of cubical homology, cohomology, and (co)homological operations via chain contraction, Using machine learning to predict catastrophes in dynamical systems, Rich Bifurcation Structure in a Two-Patch Vaccination Model

Uses Software

• CHomP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Homotopy Conley index for discrete multivalued dynamical systems
• Index pairs algorithms
• Excision-preserving cubical approach to the algorithmic computation of the discrete Conley index
• Computational homology
• The Conley index for discrete semidynamical systems
• Computer assisted method for proving existence of periodic orbits
• Conley index over the base morphism for multivalued discrete dynamical systems
• Graph approach to the computation of the homology of continuous maps
• An algorithmic approach to chain recurrence
• Open index pairs, the fixed point index and rationality of zeta functions
• Leray Functor and Cohomological Conley Index for Discrete Dynamical Systems
• A combinatorial procedure for finding isolating neighbourhoods and index pairs
• The Conley index over a base
• A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems
• Shift equivalence and the Conley index
• A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems