Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Takagi type functions and dynamical systems: the smoothness of the SBR
  measure and the existence of local time   We investigate Takagi-type functions with roughness parameter $\gamma$ that
are H\"older continuous with coefficient $H=\frac{\log\gamma}{\log \eh}.$
Analytical access is provided by an embedding into a dynamical system related
to the baker transform where the graphs of the functions are identified as
their global attractors. They possess stable manifolds hosting
Sinai-Bowen-Ruelle (SBR) measures. We show that the SBR measure is absolutely
continuous for large enough $\gamma$. Dually, where duality is related to time
reversal, we prove that for large enough $\gamma$ a version of the Takagi-type
curve centered around fibers of the associated stable manifold possesses a
square integrable local time.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: eess