@booklet {2022, title = {Doubly Intermittent Full Branch Maps with Critical Points and Singularities}, year = {2022}, keywords = {37E05, Dynamical Systems (math.DS), FOS: Mathematics}, doi = {10.48550/ARXIV.2209.12725}, url = {https://arxiv.org/abs/2209.12725}, author = {Douglas Coates and Stefano Luzzatto and Muhammad Mubarak} } @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:10.1142/S0129167X16500610, title = {A Frobenius theorem for corank-1 continuous distributions in dimensions two and three}, journal = {International Journal of Mathematics}, volume = {27}, number = {08}, year = {2016}, pages = {1650061}, abstract = {

We formulate a notion of (uniform) asymptotic involutivity and show that it implies (unique) integrability of corank-1 continuous distributions in dimensions three or less. This generalizes and extends a classical Frobenius theorem, which says that an involutive C1 distribution is uniquely integrable.

}, doi = {10.1142/S0129167X16500610}, url = {https://doi.org/10.1142/S0129167X16500610}, 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} } @article {1078-0947_2016_3_1465, title = {Young towers for product systems}, journal = {Discrete \& Continuous Dynamical Systems - A}, volume = {36}, number = {1078-0947_2016_3_146}, year = {2016}, pages = {1465}, abstract = {

We show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, H{\'e}non maps and partially hyperbolic systems.

}, issn = {1078-0947}, doi = {10.3934/dcds.2016.36.1465}, url = {http://aimsciences.org//article/id/18d4526e-470d-467e-967a-a0345ad4c642}, author = {Stefano Luzzatto and Marks Ruziboev} }