Quantitative Recurrence Near a Given Point and Dimension
نویسنده
چکیده
Quantitative recurrence indicators are defined by measuring the first entrance time of the orbit of a point x in a decreasing sequence of neighborhoods of another point y. It is proved that these recurrence indicators are a.e. greater or equal to the local dimension at y, then these recurrence indicators can be used to have a numerical upper bound on the local dimension of an invariant measure.
منابع مشابه
Quantitative recurrence properties of expanding maps
Under a map T , a point x recurs at rate given by a sequence {rn} near a point x0 if d(T(x), x0) < rn infinitely often. Let us fix x0, and consider the set of those x’s. In this paper, we study the size of this set for expanding maps and obtain its measure and sharp lower bounds on its dimension involving the entropy of T , the local dimension near x0 and the upper limit of 1 n log 1 rn . We ap...
متن کاملDimension via Waiting time and Recurrence
Quantitative recurrence indicators are defined by measuring the first entrance time of the orbit of a point x in a decreasing sequence of neighborhoods of another point y. It is proved that these recurrence indicators are a.e. greater or equal to the local dimension at y, then these recurrence indicators can be used to have a numerical upper bound on the local dimension of an invariant measure.
متن کاملHausdorff Dimension of Measures via Poincaré Recurrence
We study the quantitative behavior of Poincaré recurrence. In particular, for an equilibrium measure on a locally maximal hyperbolic set of a C diffeomorphism f , we show that the recurrence rate to each point coincides almost everywhere with the Hausdorff dimension d of the measure, that is, inf{k > 0 : fx ∈ B(x, r)} ∼ r. This result is a non-trivial generalization of work of Boshernitzan conc...
متن کاملHyperbolicity and Recurrence in Dynamical Systems: a Survey of Recent Results
We discuss selected topics of current research interest in the theory of dynamical systems, with emphasis on dimension theory, multifractal analysis, and quantitative recurrence. The topics include the quantitative versus the qualitative behavior of Poincaré recurrence, the product structure of invariant measures and return times, the dimension of invariant sets and invariant measures, the comp...
متن کاملPresenting a Model of Customer Experience Management in Mobile Banking Industry for Commercial Banks Customers in Dubai
The current research has been conducted to provide a model for customer experience management in the mobile banking industry for customers of commercial banks in Dubai. An explorative mixed methods research (qualitative and quantitative) was used in the research. Data were gathered in both qualitative phase (based on grounded theory) and quantitative phase (based on cross-sectional survey metho...
متن کامل