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PreprintCC BY-NC-ND 4.0HAL

UNIQUE ERGODICITY OF HEDGEHOGS

  • Ricardo Pérez-Marco
Open at sourcePDFDOICite

Abstract

We prove that the dynamics on a non-linearizable hedgehog is uniquely ergodic. This solves a conjecture of the author formulated in 1995. Its unique invariant probability measure is the Dirac mass at the indifferent fixed point. The proof relies on the techniques of quasi-invariant curves and the hyperbolic form of the Denjoy-Yoccoz lemma developed by the author.

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Cite

BibTeXRIS
BibTeX
@misc{perezmarco2026unique,
  title = {{UNIQUE ERGODICITY OF HEDGEHOGS}},
  author = {Ricardo Pérez-Marco},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28797},
  eprint = {2609.28797},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05761760v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - UNIQUE ERGODICITY OF HEDGEHOGS
AU  - Ricardo Pérez-Marco
PY  - 2026
DA  - 2026/09/22
PB  - HAL
DO  - 10.48550/arxiv.2609.28797
UR  - https://hal.science/hal-05761760v1
AB  - We prove that the dynamics on a non-linearizable hedgehog is uniquely ergodic. This solves a conjecture of the author formulated in 1995. Its unique invariant probability measure is the Dirac mass at the indifferent fixed point. The proof relies on the techniques of quasi-invariant curves and the hyperbolic form of the Denjoy-Yoccoz lemma developed by the author.
ER  -