2104.01947
Некоторые задачи о сохраняющих меру преобразованиях
В.В. Рыжиков
incompletemedium confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper states the theorem that ergodicity of the homoclinic (Gordin) group H(T) implies mixing of all orders and sketches a joining-based proof for k=2, citing k=1 from prior work, but does not supply the induction that yields all k. The model gives a complete, correct argument via H(T)-invariance of L2-weak limits and an induction on k.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The note gives a clear and engaging exposition connecting homoclinic groups and multiple mixing, with a correct sketch for the three-fold case and useful context. To match the stated all-orders claim, an explicit induction or an external reference should be added. Clarifying the equidecomposability step under an ergodic H(T)-action would further solidify the argument.