Special Session 103: The integrability and bifurcation theory of dynamical systems and its applications

Support measures and complex dimensions in dynamics
Goran Radunovic
University of Zagreb
Croatia
Co-Author(s):    Goran Radunovi\`c and Steffen Winter
Abstract:
The general Steiner formula of Hug, Last and Weil describes the tube volume of any closed set in R^d, and the support measures arising from this formula encode its geometric properties. Recently, basic contents and support contents have been introduced as tools to extract fractal properties of a set from these measures. The original motivation was to extract the geometric meaning of the coefficients in fractal tube formulas that arise in the theory of complex dimensions by Lapidus, Radunovic, and Zubrinic. This is achieved by introducing appropriate zeta functions associated to each support measure, which turn out to be useful tools for computing basic contents and support contents. We will reflect on applications of these new functionals to analysis of orbits of dynamical systems. Based on joint work with Steffen Winter.