Symbolic representations of nonexpansive group automorphisms
| dc.creator | Lindenstrauss, Elon | |
| dc.creator | Schmidt, Klaus | |
| dc.date | 2004-09-15 | |
| dc.date | 2005-05-18 | |
| dc.date.accessioned | 2026-07-07T05:12:09Z | |
| dc.date.available | 2026-07-07T05:12:09Z | |
| dc.description | If $α$ is an irreducible nonexpansive ergodic automorphism of a compact abelian group $X$ (such as an irreducible nonhyperbolic ergodic toral automorphism), then $α$ has no finite or infinite state Markov partitions, and there are no nontrivial continuous embeddings of Markov shifts in $X$. In spite of this we are able to construct a symbolic space $V$ and a class of shift-invariant probability measures on $V$ each of which corresponds to an $α$-invariant probability measure on $X$. Moreover, every $α$-invariant probability measure on $X$ arises essentially in this way. The last part of the paper deals with the connection between the two-sided beta-shift $V_β$ arising from a Salem number $β$ and the nonhyperbolic ergodic toral automorphism $α$ arising from the companion matrix of the minimal polynomial of $β$, and establishes an entropy-preserving correspondence between a class of shift-invariant probability measures on $V_β$ and certain $α$-invariant probability measures on $X$. This correspondence is much weaker than, but still quite closely modelled on, the connection between the two-sided beta-shifts defined by Pisot numbers and the corresponding hyperbolic ergodic toral automorphisms. | |
| dc.identifier | https://arxiv.org/abs/math/0409257 | |
| dc.identifier | http://arxiv.org/abs/math/0409257 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72481 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37A05; 37A45; 37C15; 37C29; 37H05 | |
| dc.title | Symbolic representations of nonexpansive group automorphisms | |
| dc.type | text |