11
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Statistical properties for flows with unbounded roof function, including the Lorenz attractor

      Preprint
      ,

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          For geometric Lorenz attractors (including the classical Lorenz attractor) we obtain a greatly simplified proof of the central limit theorem which applies also to the more general class of codimension two singular hyperbolic attractors. We also obtain the functional central limit theorem and moment estimates, as well as iterated versions of these results. A consequence is deterministic homogenisation (convergence to a stochastic differential equation) for fast-slow dynamical systems whenever the fast dynamics is singularly hyperbolic of codimension two.

          Related collections

          Most cited references15

          • Record: found
          • Abstract: not found
          • Article: not found

          Differentiable dynamical systems

          S Smale (1967)
            Bookmark
            • Record: found
            • Abstract: not found
            • Article: not found

            Statistical Properties of Dynamical Systems with Some Hyperbolicity

              Bookmark
              • Record: found
              • Abstract: not found
              • Article: not found

              Distribution Function Inequalities for Martingales

                Bookmark

                Author and article information

                Journal
                06 March 2018
                Article
                1803.02125
                b0f2f224-ddc0-4db1-84bc-9138c23521df

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Our old unpublished preprint "Decay of correlations for flows with unbounded roof function, including the infinite horizon planar periodic Lorentz gas" treated (a) statistical limit laws for Lorenz attractors and (b) decay of correlations for Lorentz gases. Topic (a) is completed here, replacing the old preprint. (Topic (b) is dealt with elsewhere using different methods, see arXiv:1710.02671.)
                math.DS

                Comments

                Comment on this article