Continuation sheaves in dynamics: sheaf cohomology and bifurcation
DOI10.1016/j.jde.2023.04.041zbMath1520.37018arXiv2102.02198MaRDI QIDQ6155328
K. Alex Dowling, Robert C. A. M. VanderVorst, William D. Kalies
Publication date: 12 June 2023
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2102.02198
bifurcationcontinuationsheaf cohomologycategory of dynamical systemsattractor sheafMorse representation/decomposition
Stability of topological dynamical systems (37B25) Sheaf cohomology in algebraic topology (55N30) Gradient-like behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems (37B35) Index theory for dynamical systems, Morse-Conley indices (37B30) Dynamical aspects of attractors and their bifurcations (37G35) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)
Cites Work
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- Efficient computation of Lyapunov functions for Morse decompositions
- Discrete Morse theory for computing cellular sheaf cohomology
- Lattice structures for attractors. II
- The conjugacy problem in ergodic theory
- An invitation to general algebra and universal constructions.
- Homotopy invariants of repeller-attractor pairs. II: Continuation of R-A pairs
- Remarks on Priestley duality for distributive lattices
- Algebraic topology from a homotopical viewpoint
- Quasiorders and sublattices of distributive lattices
- Global dynamics for steep nonlinearities in two dimensions
- Lattice structures for attractors. III
- Manifolds, sheaves, and cohomology
- Topological dynamical systems. An introduction to the dynamics of continuous mappings
- An algorithmic approach to chain recurrence
- Lattice structures for attractors. I
- Cohomology of isolated invariant sets under perturbation
- Conley--Morse Databases for the Angular Dynamics of Newton's Method on the Plane
- Combinatorial-topological framework for the analysis of global dynamics
- An Algorithmic Approach to Lattices and Order in Dynamics
- The Continuation Theory for Morse Decompositions and Connection Matrices
- Connected Simple Systems and The Conley Index of Isolated Invariant Sets
- A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems
- Topological Computation Analysis of Meteorological Time-Series Data
- Rigorous Computation of the Global Dynamics of Integrodifference Equations with Smooth Nonlinearities
- Combinatorial Representation of Parameter Space for Switching Networks
- On topologies for function spaces
- Equilibria and their Stability in Networks with Steep Sigmoidal Nonlinearities
