Geodesic
Rigidity properties of ℤ^{𝕕}-actions on tori and solenoids
Einsiedler, Manfred1 ; Lindenstrauss, Elon2, 3
1 Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195
2 Department of Mathematics, Stanford University, Stanford, CA 94305
3 Courant Institute of Mathematical Sciences, 251 Mercer St., New York, NY 10012
Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 99-110 Cet article a éte moissonné depuis la source American Mathematical Society

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We show that Haar measure is a unique measure on a torus or more generally a solenoid $X$ invariant under a not virtually cyclic totally irreducible $\mathbb Z^d$-action by automorphisms of $X$ such that at least one element of the action acts with positive entropy. We also give a corresponding theorem in the non-irreducible case. These results have applications regarding measurable factors and joinings of these algebraic $\mathbb Z^d$-actions.
DOI : 10.1090/S1079-6762-03-00117-3

Einsiedler, Manfred 1 ; Lindenstrauss, Elon 2, 3

1 Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195
2 Department of Mathematics, Stanford University, Stanford, CA 94305
3 Courant Institute of Mathematical Sciences, 251 Mercer St., New York, NY 10012 
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Einsiedler, Manfred; Lindenstrauss, Elon. Rigidity properties of ℤ^{𝕕}-actions on tori and solenoids. Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 99-110. doi: 10.1090/S1079-6762-03-00117-3

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