Published paper
Abstract
The paper describes weak limits of ergodic invariant probability measures for unipotent flows and supplies a linearization estimate near proper homogeneous strata.
Role in dependence graphs
Proof-critical source
The Dirichlet spectrum
This paper is included only for the following marked statement:
- Proposition 3.4 · author-manuscript fallback PDF pp. 10–11 (statement and proof)Uniform stabilizer-or-small-time alternative near a compact part of a homogeneous stratum.
AI-generated audit
Audit summary
Not a correctness certificate. These reports do not replace expert scrutiny or formal verification.
Exact reviewed source
Author-hosted manuscript · explicit fallback for inaccessible version of record
Shahar Mozes and Nimish A. Shah. On the space of ergodic invariant measures of unipotent flows. Author-hosted manuscript corresponding to Ergodic Theory and Dynamical Systems 15 (1995), no. 1, 149–159.
The Cambridge version of record was not directly retrievable. The reviewed 16-page 2010 TeX/Quartz A4 file is an author-hosted manuscript and is not represented as the 11-page publisher object; this report audits only the linked manuscript.
Open audited source ↗01Statements1 reported findingNo statement issues found
Proposition 3.4 correctly gives the one-parameter thin-neighborhood alternative used as the base case in Shah's multidimensional induction.
Proposition 3.4No issue found
The stabilizer-or-small-time alternative is uniform on compact sets
Author-manuscript PDF pp. 10–11 (statement and proof)
For a compact subset of the algebraic stratum and fixed error, the construction chooses one neighborhood so that every unipotent orbit either has a representative fixed by the flow or spends less than the prescribed proportion of all sufficiently long intervals in the corresponding compact neighborhood.
02Proofs2 reported findingsNo proof issues found
The proof is complete through the Dani–Margulis polynomial-growth and discreteness results; the paper also states that the proposition follows directly from Dani–Margulis Theorem 7.3.
Proof of Proposition 3.4No issue found in the reviewed proof
Disjoint maximal intervals and a polynomial small-value estimate give the density bound
Author-manuscript PDF pp. 10–11
Uniqueness of the nearby representative makes the maximal intervals either equal or disjoint. On each interval, the polynomial-growth estimate bounds time in the smaller neighborhood by the prescribed fraction of the full interval. Summing disjoint intervals yields the global upper density unless the representative is fixed.
Exact recursive routeDependency scope verified
The Dani–Margulis chapter is a sufficient terminal parent
Author-manuscript PDF p. 10, opening of the proof of Proposition 3.4
The manuscript explicitly notes that Proposition 3.4 follows from Dani–Margulis Theorem 7.3. Its supplied shorter proof uses the same chapter's Propositions 3.2 and 4.2, so no additional non-book parent is required for this selected branch.
03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.