TY - JOUR
T1 - A short proof of Host’s equidistribution theorem
AU - Hochman, Michael
N1 - Publisher Copyright:
© 2022, The Hebrew University of Jerusalem.
PY - 2022/12
Y1 - 2022/12
N2 - This note contains a new proof of Host’s equidistribution theorem for multiplicatively independent endomorphisms of ℝ/ℤ. The method is a simplified version of our recent work on equidistribution under toral automorphisms [2] and is related to the argument in [3], but avoids the use of the scenery flow and of Marstrand’s projection theorem, using instead a direct Fourier argument to establish smoothness of the limit measure.
AB - This note contains a new proof of Host’s equidistribution theorem for multiplicatively independent endomorphisms of ℝ/ℤ. The method is a simplified version of our recent work on equidistribution under toral automorphisms [2] and is related to the argument in [3], but avoids the use of the scenery flow and of Marstrand’s projection theorem, using instead a direct Fourier argument to establish smoothness of the limit measure.
UR - http://www.scopus.com/inward/record.url?scp=85145409282&partnerID=8YFLogxK
U2 - 10.1007/s11856-022-2444-x
DO - 10.1007/s11856-022-2444-x
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AN - SCOPUS:85145409282
SN - 0021-2172
VL - 251
SP - 527
EP - 539
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 2
ER -