TY - CHAP
T1 - Non-uniform measure rigidity for ℤk actions of symplectic type
AU - Katok, Anatole
AU - Hertz, Federico Rodriguez
N1 - Funding Information:
The work of the first author was based on research supported by NSF grants DMS-1002554. The work of the second author was partially supported by the Center for Dynamics and Geometry at Penn State and NSF grants DMS-1201326.
Publisher Copyright:
© 2017 A. Katok and F. Rodriguez Hertz.
PY - 2017
Y1 - 2017
N2 - We make a modest progress in the nonuniform measure rigidity program started in 2007 and its applications to the Zimmer program. The principal innovation is in establishing rigidity of large measures for actions of ℤk, k ≥ 2 with pairs of negatively proportional Lyapunov exponents which translates to applicability of our results to actions of lattices in higher rank semisimple Lie groups other than SL(n, ℝ), namely, Sp(2n, ℤ) and SO(n, n; ℤ).
AB - We make a modest progress in the nonuniform measure rigidity program started in 2007 and its applications to the Zimmer program. The principal innovation is in establishing rigidity of large measures for actions of ℤk, k ≥ 2 with pairs of negatively proportional Lyapunov exponents which translates to applicability of our results to actions of lattices in higher rank semisimple Lie groups other than SL(n, ℝ), namely, Sp(2n, ℤ) and SO(n, n; ℤ).
UR - http://www.scopus.com/inward/record.url?scp=85029562292&partnerID=8YFLogxK
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U2 - 10.1090/conm/692/13923
DO - 10.1090/conm/692/13923
M3 - Chapter
AN - SCOPUS:85029562292
T3 - Contemporary Mathematics
SP - 195
EP - 208
BT - Contemporary Mathematics
PB - American Mathematical Society
ER -