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August 25, 2026
Scientists Develop Algorithm for More Reliable Processors in Data Centres
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Chaotic foliations with Ehresmann connection

Journal of Geometry and Physics. 2024. Vol. 199. Article 105166.
Nina I. Zhukova

We consider smooth codimension q foliations on n-dimensional manifolds where 0<q<n. We use Ehresmann connections as a technical tool to introduce the notion of sensitivity to initial conditions for foliations. We extend Devaney's definition of chaos for cascades to foliations with Ehresmann connection. Our main result states that sensitivity to initial conditions of a foliation with Ehresmann connection follows from topological transitivity and density of minimal sets of the foliation. Compactness both minimal sets and the ambient manifold is not assumed. The results are applied to complete Cartan foliations.

Research target: Mathematics
Language: English
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Keywords: foliationEhresmann connection for a foliationchaotic foliationsensitivity to initial conditions
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