The spectrum of vector bundle flows with invariant subbundles

Author:
R. C. Swanson

Journal:
Proc. Amer. Math. Soc. **83** (1981), 141-145

MSC:
Primary 58F25; Secondary 58F19

DOI:
https://doi.org/10.1090/S0002-9939-1981-0620000-4

MathSciNet review:
620000

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Abstract: A vector bundle flow on the vector bundle over a compact metric space induces a one-parameter group of bounded operators acting on the continuous sections of , with infinitesimal generator . An example is given by the tangent flow , if is a flow on a smooth manifold. In this article, the spectrum of the generator is used to study the exponential growth rates of bundle trajectories in the neighborhood of a fixed invariant subbundle, e.g. the tangent bundle of a submanifold of . Auxiliary normal and tangential spectra are introduced, and their relationship and fine structure are explored.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0620000-4

Keywords:
Vector bundle flows,
infinitesimal generator of a semigroup,
operator theory

Article copyright:
© Copyright 1981
American Mathematical Society