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## Chaos in Cartan foliations

Chaotic foliations generalize Devaney's concept of chaos for

dynamical systems. The property of a foliation to

be chaotic is transversal. The existence problem of chaos for a Cartan foliation

is reduced to the corresponding problem for its holonomy pseudogroup of

local automorphisms of a transversal manifold. Chaotic foliations with transversal Cartan

structures are investigated.

A Cartan $(\Phi,X)$-foliation $(M, F)$ that admits an Ehresmann connection is

covered by a locally trivial bundle, and the global holonomy group of $(M, F)$

is defined. In this case, the problem is reduced to the level of

the global holonomy group of the foliation, which is a countable discrete subgroup of the

Lie group of automorphisms of some simply connected Cartan $(\Phi,X)$-manifold.

Several classes of Cartan foliations that cannot be chaotic, are indicated.

Examples of chaotic Cartan foliations are constructed.