Mathematics

In this thesis, the main aim is to study the integrability properties of continuous
tangent sub-bundles, especially those that arise in the study of dynamical systems.
After the introduction and examples part we start by studying integrability
of such sub-bundles under different regularity and dynamical assumptions.
Then we formulate a continuous version of the classical Frobenius theorem
and state some applications to such bundles, to ODE and PDE.
Finally we close of by stating some ongoing work related to interactions
between integrability, sub-Riemannian geometry and contact geometry.

34833

MAT/05