Continuation Sheaves in Dynamics: Sheaf Cohomology and Bifurcation

• Published in: arXiv.org
• Main Authors: Dowling, K, Kalies, W D, R C A M Vandervorst
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 03.02.2021
• Subjects: Algebra; Bifurcations; Chaos theory; Dynamical systems; Group theory; Homology; Invariants; Lattices; Ring structures; Set theory; Sheaves

Continuation of algebraic structures in families of dynamical systems is described using category theory, sheaves, and lattice algebras. Well-known concepts in dynamics, such as attractors or invariant sets, are formulated as functors on appropriate categories of dynamical systems mapping to categor...