English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We investigate Takagi-type functions with roughness parameter $\gamma$ thatare H\"older continuous with coefficient $H=\frac{\log\gamma}{\log \eh}.$Analytical access is provided by an embedding into a dynamical system relatedto the baker transform where the graphs of the functions are identified astheir global attractors. They possess stable manifolds hostingSinai-Bowen-Ruelle (SBR) measures. We show that the SBR measure is absolutelycontinuous for large enough $\gamma$. Dually, where duality is related to timereversal, we prove that for large enough $\gamma$ a version of the Takagi-typecurve centered around fibers of the associated stable manifold possesses asquare integrable local time.

Takagi type functions and dynamical systems: the smoothness of the SBR measure and the existence of local time