When we have a proper action of a Lie group on a manifold, it is well known that we get a stratification by orbit types and it is known that this stratification satisfies the Whitney (b) condition. In a previous article we have seen that the stratification satisfies the strong Verdier condition. In this article we improve this result and obtain smooth local triviality.
Positivity, monotonicity, and consensus on Lie groups
A refinement of Sharkovskii's theorem on orbit types characterized by two parameters
Variational discretization of thermodynamical simple systems on Lie groups
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