Speaker
Description
We investigate geometric properties of Weierstrass curves with two
components, representing series based on trigonometric functions. They
are seen to be 12 − Hölder continuous, and are not (para-)controlled
with respect to each other in the sense of the recently established
Fourier analytic approach of rough path analysis. Their graph is rep-
resented as an attractor of a smooth random dynamical system. For
one-dimensional versions we show existence of a local time and smooth-
ness of the Sinai-Bowen-Ruelle (SBR) measure. Our argument that its
graph has Hausdorff dimension 2 is in the spirit of Ledrappier-Young’s
approach of the Hausdorff dimension of attractors. This is joint work
with G. dos Reis (U Edinburgh) and A. Réveillac (U Toulouse).
