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Strong Positive Recurrence for Strongly Entropy Expanding Maps

  • Alexandre Delplanque
  • Hengyi Li
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Abstract

We introduce expanding strong positive recurrence (expanding-SPR) for non-invertible systems with critical points. We then give a sufficient condition for maps to be SPR: strong entropy expansion (SEE). We prove that expanding-SPR implies good thermodynamical properties, including exponential decay of correlations of Hölder observables for the measures of maximal entropy. The class of maps that are SEE includes all C^{\infty}-interval maps with h_{top}(f )>0 and all Viana maps.

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Cite

BibTeXRIS
BibTeX
@misc{delplanque2026strong,
  title = {{Strong Positive Recurrence for Strongly Entropy Expanding Maps}},
  author = {Alexandre Delplanque and Hengyi Li},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29814},
  eprint = {2610.29814},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29814},
}
RIS
TY  - UNPB
TI  - Strong Positive Recurrence for Strongly Entropy Expanding Maps
AU  - Alexandre Delplanque
AU  - Hengyi Li
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29814
UR  - https://arxiv.org/abs/2610.29814
AB  - We introduce expanding strong positive recurrence (expanding-SPR) for non-invertible systems with critical points. We then give a sufficient condition for maps to be SPR: strong entropy expansion (SEE). We prove that expanding-SPR implies good thermodynamical properties, including exponential decay of correlations of Hölder observables for the measures of maximal entropy. The class of maps that are SEE includes all C^{\infty}-interval maps with h_{top}(f )>0 and all Viana maps.
ER  -