Since its introduction by Felix Hausdorff in 1919, the concept of the Hausdorff dimension of sets and measures has been a versatile and powerful tool in classical analysis, geometry and geometric measure theory, mathematical physics and their numerous applications. However, there has been a particularly important symbiosis between dynamical systems and dimension theory. This connection arises both from application of dimension theory to the classification and geometric analysis of dynamical systems (and their invariant sets and measures), and the fact that many classical objects of study in mathematics arise from (sometimes implicit) dynamical systems, which often play a role in the dimension theory of said objects.

Recently, there has been substantial progress on a number of central problems in dimension theory, and while many old problems remain, many new ones have also presented themselves. These include a deeper understanding of the relationship between dimension, entropy and... (more)

A surprising discovery of 20th century mathematics is that many deterministic systems exhibit random behavior. One early example of a chaotic system was Lorenz equation used by meteorologist Edward Lorenz as a simplified model of atmospheric convection. One of the most common mechanisms of stochasticity is the Smale horseshoe appearing near a homoclinic intersection.

The Lorentz attractor and Smale horseshoe are typical examples of fractal invariant sets for dynamical systems. Fractal objects are ubiquitous in dynamics, including invariant sets, invariant measures, invariant foliations et cetera.

Thermodynamical formalism is a powerful tool for studying dimensions of fractal objects. It originated in statistical mechanics, but currently it has applications to many areas of mathematics including spectral theory, hyperbolic geometry and probability theory.

The goal of this conference is to bring together experts studying fractal objects in dynamics in order to review recent progress... (more)

Numerical computations have always played an important role in the development of the theory of Differential Equations and Dynamical Systems, more and more so as the availability and power of computers has increased dramatically over the last few decades. At the same time, the limitations of computer-assisted numerical calculations have also become increasingly apparent. Notwithstanding their enormous power, the intrinsic finite resolution of computers can lead to significant errors, especially as a result of a large number of calculations through which small errors can accumulate.

An important and growing approach to certain mathematical problems consists of developing rigorous numerical techniques in combination with more classical analytic methods in order to obtain rigorous qualitative and quantitative results. In some cases this leads to the proof of deep mathematical theorems and in other cases to quantitative, and thus more concrete and applicable, versions of abstract... (more)