Continuation sheaves in dynamics: Sheaf cohomology and bifurcation

K Alex Dowling,William D Kalies,Robert C.A.M Vandervorst

doi:10.1016/j.jde.2023.04.041

Continuation sheaves in dynamics: Sheaf cohomology and bifurcation

K Alex Dowling, William D Kalies + Show 1 more

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https://doi.org/10.1016/j.jde.2023.04.041

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Journal: Journal of Differential Equations	Publication Date: May 12, 2023
License type: publisher-specific-oa

Affiliation: Rutgers, The State University of New Jersey, Florida Atlantic University, Vrije Universiteit Amsterdam

#Sheaf Cohomology #Algebraic Structures + Show 6 more

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Abstract

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

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