00500nas a2200145 4500008004100000245008000041210006900121653001000190653003200200653002100232100002000253700002200273700002200295856003700317 2022 eng d00aDoubly Intermittent Full Branch Maps with Critical Points and Singularities0 aDoubly Intermittent Full Branch Maps with Critical Points and Si10a37E0510aDynamical Systems (math.DS)10aFOS: Mathematics1 aCoates, Douglas1 aLuzzatto, Stefano1 aMubarak, Muhammad uhttps://arxiv.org/abs/2209.1272501112nas a2200157 4500008004100000245007700041210006900118260003100187300001400218490000700232520054200239100002200781700001800803700002400821856010900845 2017 eng d00aIntegrability of dominated decompositions on three-dimensional manifolds0 aIntegrability of dominated decompositions on threedimensional ma bCambridge University Press a606–6200 v373 a
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.
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.
1 aLuzzatto, Stefano1 aTüreli, Sina1 aWar, Khadim, Mbacke uhttps://doi.org/10.1142/S0129167X1650061000676nas a2200157 4500008004100000245004500041210004500086260002100131300001000152490000700162520023500169100002200404700001800426700002400444856005000468 2016 eng d00aIntegrability of C1 invariant splittings0 aIntegrability of C1 invariant splittings bTaylor & Francis a79-880 v313 aWe 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.
1 aLuzzatto, Stefano1 aTüreli, Sina1 aWar, Khadim, Mbacke uhttps://doi.org/10.1080/14689367.2015.105748000968nas a2200145 4500008004100000022001400041245003700055210003700092300000900129490000700138520055900145100002200704700002000726856007600746 2016 eng d a1078-094700aYoung towers for product systems0 aYoung towers for product systems a14650 v363 aWe 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, Hénon maps and partially hyperbolic systems.
1 aLuzzatto, Stefano1 aRuziboev, Marks uhttp://aimsciences.org//article/id/18d4526e-470d-467e-967a-a0345ad4c642