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Effective equidistribution of large dimensional measures on affine invariant submanifolds

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arxiv 2306.06740 v2 pith:ESMSASR6 submitted 2023-06-11 math.DS math.GT

Anthony Sanchez This is my paper · ORCID
classification math.DSmath.GT
keywords effectiveinvariantmeasuresaffineequidistributionfoliationlargesubmanifolds
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The unstable foliation, that locally is given by changing horizontal components of period coordinates, plays an important role in study of translation surfaces, including their deformation theory and in the understanding of horocycle invariant measures. In this article we show that measures of large dimension on the unstable foliation equidistribute in affine invariant submanifolds and give an effective rate. An analogous result in the setting of homogeneous dynamics is crucially used in the effective density and equidistribution results of Lindenstrauss-Mohammadi and Lindenstrauss--Mohammadi--Wang.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Effective Exponential Drifts on Strata of Abelian Differentials

    math.DS 2025-01 conditional novelty 7.0 of 10

    For the stratum H(2) of translation surfaces, long horocycle orbits have discrete transverse dimension arbitrarily close to 1, with effective exponential error rates.

  2. Orbits in Teichm\"uller dynamics admits a critical exponent gap

    math.DS 2024-11 conditional novelty 7.0 of 10

    For every genus, any SL2(R)-orbit in the moduli space of flat surfaces whose stabilizer is not a lattice has critical exponent at most 1 - ε_g, a uniform gap.

  3. Quantitative finiteness of hyperplanes in hybrid manifolds

    math.DS 2025-06 conditional novelty 6.0 of 10

    For Gromov-Piatetski-Shapiro hybrid hyperbolic n-manifolds, the number of codimension-one totally geodesic hyperplanes is bounded by an explicit (if weak) function of volume and dynamical constants.

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