• Corpus ID: 231786326

Continuation Sheaves in Dynamics: Sheaf Cohomology and Bifurcation

  title={Continuation Sheaves in Dynamics: Sheaf Cohomology and Bifurcation},
  author={Kenneth Dowling and William D. Kalies and Robert C. Vandervorst},
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 categories of lattices, posets, rings or abelian groups. Sheaves are constructed from such functors, which encode data about the continuation of structure as system parameters vary. Similarly, morphisms for… 

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