TY - JOUR
T1 - Multi-invariant measures and subsets on nilmanifolds
AU - Wang, Zhiren
N1 - Publisher Copyright:
© 2018, Hebrew University Magnes Press.
PY - 2018/6/1
Y1 - 2018/6/1
N2 - Given a Zr-action α on a nilmanifold X by automorphisms and an ergodic α-invariant probability measure μ, we show that μ is the uniform measure on X unless, modulo finite index modification, one of the following obstructions occurs for an algebraic factor action(1)the factor measure has zero entropy under every element of the action(2)the factor action is virtually cyclic.We also deduce a rigidity property for invariant closed subsets.
AB - Given a Zr-action α on a nilmanifold X by automorphisms and an ergodic α-invariant probability measure μ, we show that μ is the uniform measure on X unless, modulo finite index modification, one of the following obstructions occurs for an algebraic factor action(1)the factor measure has zero entropy under every element of the action(2)the factor action is virtually cyclic.We also deduce a rigidity property for invariant closed subsets.
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U2 - 10.1007/s11854-018-0041-z
DO - 10.1007/s11854-018-0041-z
M3 - Article
AN - SCOPUS:85050154331
SN - 0021-7670
VL - 135
SP - 123
EP - 183
JO - Journal d'Analyse Mathematique
JF - Journal d'Analyse Mathematique
IS - 1
ER -