Morse decompositions and spectra on flag bundles (Q1863013)

Linear flows on vector bundles arise in linear differential equations with almost-periodic coefficients, linearized autonomous differential equations, and bilinear and linear control systems. For such flows, chain recurrent components of the induced flows on flag bundles and the corresponding Morse spectrum are constructed. The methods used for the chain recurrent components of linear flows in projective bundles and the Morse spectrum are generalized to a higher-dimension case, based on a classification of chain recurrent components for the induced flows on flag and Grassmann bundles giving the finest Morse decomposition.