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June  2017, 24: 64-67. doi: 10.3934/era.2017.24.007

A note on parallelizable dynamical systems

Josiney A. Souza 1, , Tiago A. Pacifico 1, and  Hélio V. M. Tozatti 2,

1. 

Departamento de Matemática, Universidade Estadual de Maringá, Maringá-PR, Brasil
2. 

Departamento de Matemática, Universidade Tecnolgica Federal do Paraná, Campo Mourõ-PR, Brasil

Received  February 24, 2017 Published  June 2017

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.

Keywords: Parallelizability, principal bundles.
Mathematics Subject Classification: 37C75, 34C27, 34D05, 93D05.
Citation: Josiney A. Souza, Tiago A. Pacifico, Hélio V. M. Tozatti. A note on parallelizable dynamical systems. Electronic Research Announcements, 2017, 24: 64-67. doi: 10.3934/era.2017.24.007
References:
[1]

N. P. Bhatia and G. P. Szegö, Stability Theory of Dynamical Systems, Springer-Verlag, Berlin, 1970. Google Scholar

[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. Google Scholar

[3]

O. Hájek, Parallelizability revisited, Proc. Amer. Math. Soc., 27 (1971), 77-84. doi: 10.1090/S0002-9939-1971-0271925-7. Google Scholar

[4]

D. Husemoller, Fibre Bundles, Graduate Texts in Mathematics, Springer-Verlag, New York, 1994. doi: 10.1007/978-1-4757-2261-1. Google Scholar

[5]

N. Steenrod, The Topology of Fibre Bundles, Princeton University Press, Princeton, 1951. Google Scholar

show all references

References:
[1]

N. P. Bhatia and G. P. Szegö, Stability Theory of Dynamical Systems, Springer-Verlag, Berlin, 1970. Google Scholar

[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. Google Scholar

[3]

O. Hájek, Parallelizability revisited, Proc. Amer. Math. Soc., 27 (1971), 77-84. doi: 10.1090/S0002-9939-1971-0271925-7. Google Scholar

[4]

D. Husemoller, Fibre Bundles, Graduate Texts in Mathematics, Springer-Verlag, New York, 1994. doi: 10.1007/978-1-4757-2261-1. Google Scholar

[5]

N. Steenrod, The Topology of Fibre Bundles, Princeton University Press, Princeton, 1951. Google Scholar

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