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Simultaneous equidistributing and non-dense points for non-commuting toral automorphisms

Published online by Cambridge University Press:  11 May 2018

MANFRED EINSIEDLER  and
ALEX MAIER
MANFRED EINSIEDLER
Affiliation:
ETH Zürich, Departement Mathematik, Rämistrasse 101, 8092 Zürich, Switzerland email manfred.einsiedler@math.ethz.ch, alex.georg.maier@gmail.com
ALEX MAIER
Affiliation:
ETH Zürich, Departement Mathematik, Rämistrasse 101, 8092 Zürich, Switzerland email manfred.einsiedler@math.ethz.ch, alex.georg.maier@gmail.com
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Abstract

We show in prime dimension that for two non-commuting totally irreducible toral automorphisms the set of points that equidistribute under the first map but have non-dense orbit under the second has full Hausdorff dimension. In non-prime dimension the argument fails only if the automorphisms have strong algebraic relations.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 1 , January 2020 , pp. 175 - 193
Copyright
© Cambridge University Press, 2018 

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