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PreprintarXiv licencearXiv

Period spectrum and rigidity of interval maps

  • Gabriel Fuhrmann
  • Maik Gröger
  • Alejandro Passeggi
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Abstract

We study the extent to which periodic orbits determine a one-dimensional dynamical system. In particular, we show that they determine every topologically mixing interval map. More generally, for a non-mixing interval map f with dense periodic points, the periodic orbits need not determine f, but they always do so for f2. Finally, for maps on compact intervals, we obtain a local version of this rigidity: for each basic set B arising in the spectral decomposition of an interval map f, there exists an iterate fq whose restriction to B is determined by the periodic orbits of f.

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Cite

BibTeXRIS
BibTeX
@misc{fuhrmann2026period,
  title = {{Period spectrum and rigidity of interval maps}},
  author = {Gabriel Fuhrmann and Maik Gröger and Alejandro Passeggi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07435},
  eprint = {2610.07435},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07435},
}
RIS
TY  - UNPB
TI  - Period spectrum and rigidity of interval maps
AU  - Gabriel Fuhrmann
AU  - Maik Gröger
AU  - Alejandro Passeggi
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.07435
UR  - https://arxiv.org/abs/2610.07435
AB  - We study the extent to which periodic orbits determine a one-dimensional dynamical system. In particular, we show that they determine every topologically mixing interval map. More generally, for a non-mixing interval map f with dense periodic points, the periodic orbits need not determine f, but they always do so for f^2. Finally, for maps on compact intervals, we obtain a local version of this rigidity: for each basic set B arising in the spectral decomposition of an interval map f, there exists an iterate f^q whose restriction to B is determined by the periodic orbits of f.
ER  -