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Emergence of partially hyperbolic skew-products with circle fibers

  • Odylo Costa
  • Mauricio Poletti
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Abstract

We study the statistical behavior of partially hyperbolic skew-products over Axiom A diffeomorphisms using emergence. Generically, these systems satisfy the Palis conjecture: they have a finite number of physical measures whose basins together have full volume. In particular, for Lebesgue almost every point, the empirical measures converge to one of finitely many physical measures. We study the non-generic case and prove that, even when the sequence of empirical measures may have uncountably many accumulation points, these systems have low emergence.

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Cite

BibTeXRIS
BibTeX
@misc{costa2026emergence,
  title = {{Emergence of partially hyperbolic skew-products with circle fibers}},
  author = {Odylo Costa and Mauricio Poletti},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20946},
  eprint = {2610.20946},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20946},
}
RIS
TY  - UNPB
TI  - Emergence of partially hyperbolic skew-products with circle fibers
AU  - Odylo Costa
AU  - Mauricio Poletti
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20946
UR  - https://arxiv.org/abs/2610.20946
AB  - We study the statistical behavior of partially hyperbolic skew-products over Axiom A diffeomorphisms using emergence. Generically, these systems satisfy the Palis conjecture: they have a finite number of physical measures whose basins together have full volume. In particular, for Lebesgue almost every point, the empirical measures converge to one of finitely many physical measures. We study the non-generic case and prove that, even when the sequence of empirical measures may have uncountably many accumulation points, these systems have low emergence.
ER  -