@article {luzzatto_2017, title = {Integrability of dominated decompositions on three-dimensional manifolds}, journal = {Ergodic Theory and Dynamical Systems}, volume = {37}, number = {2}, year = {2017}, pages = {606{\textendash}620}, publisher = {Cambridge University Press}, abstract = {


We investigate the integrability of two-dimensional invariant distributions (tangent sub-bundles) which arise naturally in the context of dynamical systems on 3-manifolds. In particular, we prove unique integrability of dynamically dominated and volume-dominated Lipschitz continuous invariant decompositions as well as distributions with some other regularity conditions.

}, doi = {10.1017/etds.2015.64}, author = {Stefano Luzzatto and Sina T{\"u}reli and Khadim Mbacke War} } @article {doi:10.1080/14689367.2015.1057480, title = {Integrability of C1 invariant splittings}, journal = {Dynamical Systems}, volume = {31}, number = {1}, year = {2016}, pages = {79-88}, publisher = {Taylor \& Francis}, abstract = {

We derive some new conditions for integrability of dynamically defined C1 invariant splittings, formulated in terms of the singular values of the iterates of the derivative of the diffeomorphism which defines the splitting.

}, doi = {10.1080/14689367.2015.1057480}, url = {https://doi.org/10.1080/14689367.2015.1057480}, author = {Stefano Luzzatto and Sina T{\"u}reli and Khadim Mbacke War} } @mastersthesis {2015, title = {Integrability of Continuous Tangent Sub-bundles}, year = {2015}, school = {SISSA}, abstract = {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.}, keywords = {Dynamical Systems, Global Analysis, Frobenius Theorem, Integrability}, url = {http://urania.sissa.it/xmlui/handle/1963/34630}, author = {Sina T{\"u}reli} }