Parameter dependent pull-back of closed differential forms and invariant integrals
Keywords
Differential forms, invariant integrals, bifurcation, Kelvin theorem, Helmholtz theoremAbstract
We prove, given a closed differential $k$-form $\omega$ in an arbitrary open set $D \subset {\mathbb R}^n$, and a parameter dependent smooth map $F(\cdot,\lambda)$ from an arbitrary open set $G \subset {\mathbb R}^m$ into $D$, that the derivative with respect to $\lambda$ of the pull-back $F(\cdot,\lambda)^{*}\omega$ is exact in $G$. We give applications to various theorems in topology, dynamics and hydrodynamics.Downloads
Published
2005-09-01
How to Cite
1.
MAWHIN, Jean. Parameter dependent pull-back of closed differential forms and invariant integrals. Topological Methods in Nonlinear Analysis. Online. 1 September 2005. Vol. 26, no. 1, pp. 17 - 33. [Accessed 18 April 2024].
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