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Sofic systems and extreme points of self-affine limit sets

  • Stefano Silvestri
  • Rodrigo A. Pérez
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Abstract

Given any iterated function system (IFS) on the plane whose affine transformations share the same contracting matrix T, we characterize the set of extreme points of the attractor A (along the convex hull conv(A)) in terms of a directed graph on the edges of conv(A). This graph corresponds to a sofic system on the coding space associated to the IFS. When T is proper orthogonal or purely real, we give conditions for conv(A) to be a finite polygon and, under additional symmetry of the transformations, we give conditions for A itself to coincide with conv(A).

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Cite

BibTeXRIS
BibTeX
@misc{silvestri2026sofic,
  title = {{Sofic systems and extreme points of self-affine limit sets}},
  author = {Stefano Silvestri and Rodrigo A. Pérez},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23174},
  eprint = {2609.23174},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23174},
}
RIS
TY  - UNPB
TI  - Sofic systems and extreme points of self-affine limit sets
AU  - Stefano Silvestri
AU  - Rodrigo A. Pérez
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.23174
UR  - https://arxiv.org/abs/2609.23174
AB  - Given any iterated function system (IFS) on the plane whose affine transformations share the same contracting matrix T, we characterize the set of extreme points of the attractor A (along the convex hull conv(A)) in terms of a directed graph on the edges of conv(A). This graph corresponds to a sofic system on the coding space associated to the IFS. When T is proper orthogonal or purely real, we give conditions for conv(A) to be a finite polygon and, under additional symmetry of the transformations, we give conditions for A itself to coincide with conv(A).
ER  -