Oct 19 – 20, 2017
INSA Toulouse
Europe/Paris timezone

On the Hausdorff dimension of a very rough Weierstrass curve whose components are not controlled

Oct 20, 2017, 5:00 PM
Salle 13 Bâtiment Mathématiques Appliquées (INSA Toulouse)

Salle 13 Bâtiment Mathématiques Appliquées

INSA Toulouse

INSA Toulouse Département Mathématiques Appliquées 135 avenue de Rangueil 31077 Toulouse Cédex 4


Peter Imkeller


We investigate geometric properties of Weierstrass curves with two components, representing series based on trigonometric functions. They are seen to be $\frac12$-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 represented as an attractor of a smooth random dynamical system. 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 O. Pamen (U Liverpool and AIMS Ghana).

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