Continuation sheaves in dynamics: Sheaf cohomology and bifurcation

Algebraic structures such as the lattices of attractors, repellers, and Morse representations provide a computable description global dynamics. In this paper, sheaf-theoretic approach to their continuation is developed. The algebraic are cast into categorical framework study systematically simultaneously. Sheaves built from abstract formulation, which track data systems vary. Sheaf cohomology computed for several classical bifurcations, demonstrating its ability detect classify bifurcations.