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The Geometry of the Flux

  • Augustin Banyaga
Part of the Mathematics and Its Applications book series (MAIA, volume 400)

Abstract

Let φ t ∈ Diff c (M) be an isotopy (with φ0 = id M ). We defined in 1.1 a family of vector fields \(\dot \varphi = {\xi _t}\) on M by:
$$\frac{{d{\varphi _t}}}{{dt}}\left( x \right) = {\xi _t}\left( {{\varphi _t}\left( x \right)} \right)$$
(1)
We get back the isotopy φ t by integrating the time dependent ordinary differential equations above defining ξ t .

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Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Augustin Banyaga
    • 1
  1. 1.Department of MathematicsThe Pennsylvania State UniversityUSA

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