Published paper
Abstract
The paper studies limit distributions of polynomial trajectories on finite-volume homogeneous spaces. Its quantitative return theorem and linearization theorem extend unipotent one-parameter arguments to polynomial maps and isolate concentration near proper homogeneous subspaces.
Role in dependence graphs
Proof-critical source
The Dirichlet spectrum
This paper is included only for the following marked statements:
- Theorem 3.1 · Duke Mathematical Journal 75 (1994), Section 3Quantitative non-divergence for polynomial trajectories.
- Theorem 5.2 and Proposition 5.4 · Duke Mathematical Journal 75 (1994), Section 5Linearization near a proper homogeneous stratum and the one-parameter base case.
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Audit summary
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Exact reviewed source
Exact version of record hosted by an author · Duke Mathematical Journal 75 (1994), 711–732
Nimish A. Shah. Limit distributions of polynomial trajectories on homogeneous spaces. Duke Mathematical Journal 75 (1994), no. 3, 711–732.
Open audited source ↗01Statements2 reported findingsNo statement issues found
The polynomial-trajectory recurrence theorem and the linearization alternative used downstream are correctly formulated.
Theorem 3.1No issue found
Quantitative return extends from one parameter to polynomial boxes
Printed pages 716–718
Dani–Margulis Theorem 6.1 uses only the bounded-degree polynomial control needed here. Applying it on every radial slice and integrating in polar coordinates gives the displayed higher-dimensional estimate.
Theorem 5.2 and Proposition 5.4No issue found
The thin-neighborhood alternative has the stated quantifiers
Printed pages 723–727
The induction on the dimension of the homogeneous stratum separates concentration on a smaller stabilizer from small relative time in the chosen neighborhood. The conclusion is exactly the form used by Shah 1996.
02Proofs2 reported findingsNo proof issues found
The selected proof chain is complete through the Dani–Margulis chapter and the one-parameter base case of Mozes–Shah.
Multidimensional inductionNo issue found in the reviewed proof
The one-parameter base is not omitted
Printed pages 723–727
The paper explicitly takes the one-dimensional case from Mozes–Shah Proposition 3.4 and builds the higher-dimensional statement by induction. The remaining algebraic-discreteness and polynomial-growth inputs are the numbered Dani–Margulis chapter results listed in the proof.
Recursive source boundaryDependency scope verified
Ratner is not a necessary parent for the selected statement
Sections 4–5
Ratner's theorem appears in the paper's broader limit-measure argument. The selected linearization alternative closes through Dani–Margulis and Mozes–Shah; no Ratner classification statement is invoked in that branch.
03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.