Hausdorff dimension of Gauss–Cantor sets and two applications to classical Lagrange and Markov spectra

Hausdorff Dimension, Lagrange and Markov Dynamical Spectra for Geometric Lorenz Attractors

In this paper, we show that geometric Lorenz attractors have Hausdorff dimension strictly greater than 2. We use this result to show that for a “large” set of real functions the Lagrange and Markov Dynamical spectrum associated to these attractors has persistently non-empty interior.

Fractal sets and Hausdorff dimension

We consider Farey series of rational numbers in terms of fractal sets labeled by the Hausdorff dimension with values defined in the interval 1 < h < 2 and associated with fractal curves. Our results come from the observation that the fractional quantum Hall effect-FQHE occurs in pairs of dual topological quantum numbers, the filling factors. These quantum numbers obey some properties of the Far...

dedekind modules and dimension of modules

در این پایان نامه، در ابتدا برای مدول ها روی دامنه های پروفر شرایط معادل به دست آورده ایم و خواصی از ددکیند مدول ها روی دامنه های پروفر مشخص کرده ایم. در ادامه برای ددکیند مدول های با تولید متناهی روی حلقه های به طور صحیح بسته شرایط معادل به دست آورده ایم و ددکیند مدول های ضربی را مشخص کرده ایم. گزاره هایی در مورد بعد ددکیند مدول ها بیان کرده ایم. در پایان، قضایای lying over و going down را برا...

Hausdorff Dimension and Its Applications

The theory of Hausdorff dimension provides a general notion of the size of a set in a metric space. We define Hausdorff measure and dimension, enumerate some techniques for computing Hausdorff dimension, and provide applications to self-similar sets and Brownian motion. Our approach follows that of Stein [4] and Peres [3].

Calculating Hausdorff Dimension of Julia Sets and Kleinian Limit Sets