Taking the Measure of One-Dimensional Dynamics

One-dimensional dynamics has become a vast area, exploiting tools from complex analysis, Diophantine approximation, ergodic theory and operator theory. It is remarkable as well as reassuring that many of the conjectured features of one-dimensional systems are by now rigorously proven, although many questions, some major conjectures among them, remain open. To mention a few:

- MLC (is the Mandelbrot set locally connected?) is still wide open and the structure of the Multibrot set (Mandelbrot set for for higher degree polynomials) is still poorly understood. - Many of the fine details of real one-dimensional dynamics are proved by complex dynamics, but remain unproved for non-analytic smooth maps. - The Palis Conjecture, i.e., denseness of hyperbolicity, has been solved for complex polynomials, but what is the situation for rational maps? -Can the structures found in one-dimensional dynamics be applied in higher dimensional settings. Several results exist for dissipative Henon maps, Lorenz maps, etc., but many more questions lie wide open.

The central part of the workshop consists of invited talks that have a general flavor.