# 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.

## One Citation

On the global behavior of linear flows

- Mathematics
- 2022

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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