Self Affine Delone Sets and Deviation Phenomena

  title={Self Affine Delone Sets and Deviation Phenomena},
  author={Scott Schmieding and Rodrigo Trevi{\~n}o},
  journal={Communications in Mathematical Physics},
We study the growth of norms of ergodic integrals for the translation action on spaces coming from expansive, self-affine Delone sets. The linear map giving the self-affinity induces a renormalization map on the pattern space and we show that the rate of growth of ergodic integrals is controlled by the induced action of the renormalizing map on the cohomology of the pattern space up to boundary errors. We explore the consequences for the diffraction of such Delone sets, and explore in detail… 
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