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A note on parallelizable dynamical systems

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  • Hájek [3] showed that a dynamical system on a Tychonoff space with paracompact orbit space is parallelizable if and only if its corresponding bundle is a locally trivial fiber bundle with fiber $\mathbb{R}$. The present paper provides an enhancement for this classical theorem by omitting all topological hypotheses.

    Mathematics Subject Classification: 37C75, 34C27, 34D05, 93D05.


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  • [1] N. P. Bhatia and G. P. Szegö, Stability Theory of Dynamical Systems, Springer-Verlag, Berlin, 1970.
    [2] J. Dugundji and H. A. Antosiewicz, Parallelizable flows and Lyapunov's second method, Ann. of Math., 73 (1961), 543-555.  doi: 10.2307/1970316.
    [3] O. Hájek, Parallelizability revisited, Proc. Amer. Math. Soc., 27 (1971), 77-84.  doi: 10.1090/S0002-9939-1971-0271925-7.
    [4] D. Husemoller, Fibre Bundles, Graduate Texts in Mathematics, Springer-Verlag, New York, 1994. doi: 10.1007/978-1-4757-2261-1.
    [5] N. Steenrod, The Topology of Fibre Bundles, Princeton University Press, Princeton, 1951.
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