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Equiregular Distribution


An equiregular distribution is a smooth distribution for which the dimension of each successive span of iterated Lie brackets is constant over the manifold. For a bracket-generating distribution Delta, write Delta^j(q) for the span of brackets of length at most j at q. Equiregularity means that the growth vector (dimDelta^1(q),...,dimDelta^s(q)) is independent of q (Wang and Zelenko 2026).

Wang and Zelenko (2026) constructed an equiregular rank-two example with growth vector (2,3,5,8,9) on a manifold diffeomorphic to R^9 for which the sub-Riemannian Sard conjecture fails.


See also

Bracket-Generating Distribution, Smooth Distribution, Sub-Riemannian Sard Conjecture

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References

Wang, B. and Zelenko, I. "An Equiregular Counterexample to the Sard Conjecture for Sub-Riemannian Endpoint Maps." 16 Oct 2026. https://arxiv.org/abs/2610.24080.

Cite this as:

Weisstein, Eric W. "Equiregular Distribution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EquiregularDistribution.html

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