Aug 28 – 31, 2018
Angers - France
Europe/Paris timezone

On the geometry of very rough Weierstrass curves: local time, SBR measure, Hausdorff dimension

Aug 30, 2018, 9:10 AM
Angers - France

Angers - France


Peter Imkeller (Mathematisches Institut der Humboldt-Universität zu Berlin)


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).

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