February 3, 2022

On the geometry of some rough Weierstrass and Takagi type curves: SBR measure and local time

Speaker: Prof. Dr. Peter Imkeller (Institute for Mathematics, Humboldt-University of Berlin, Germany)

Abstract: We investigate geometric properties of graphs of Weierstrass or Takagi type functions, represented by series based on smooth functions. They are Hölder continuous, and can be embedded into smooth dynamical systems, where their graphs emerge as pullback attractors. It turns out that occupation measures and Sinai-Bowen-Ruelle (SBR)
measures on their stable manifolds are dual by time reversal. A suitable version of approximate self-similarity for deterministic functions allows to ”telescope” small scale properties from macroscopic ones. As a consequence, absolute continuity of the SBR measure is seen to be dual to the existence of local time. The link between the rough
curves considered and smooth dynamical systems can be generalized in various ways. Applications to regularization of singular ODE by rough signals are on our agenda.

This is joint work with O. Pamen (U Liverpool and AIMS Ghana) and G. dos Reis (U Edinburgh).

Coordinator: Donatien Wilfried Kuissi Kamdem

Join via Zoom HERE

Meeting ID: 926 0538 0740
Passcode: 107706

The slides for the talk will be made available to interested participants only after the talk and upon request.