The Selgrade Decomposition for Linear Semiflows on Banach Spaces

@article{Blumenthal2017TheSD,
  title={The Selgrade Decomposition for Linear Semiflows on Banach Spaces},
  author={Alex Blumenthal and Yuri Latushkin},
  journal={Journal of Dynamics and Differential Equations},
  year={2017},
  volume={31},
  pages={1427-1456}
}
We extend Selgrade’s Theorem, Morse spectrum, and related concepts to the setting of linear skew product semiflows on a separable Banach bundle. We recover a characterization, well-known in the finite-dimensional setting, of exponentially separated subbundles as attractor–repeller pairs for the associated semiflow on the projective bundle. 
1 Citations
On the global behavior of linear flows
For linear flows on vector bundles, it is analyzed when subbundles in the Selgrade decomposition yield chain transitive subsets for the induced flow on the associated Poincaré sphere bundle.

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