Expansive subdynamics for algebraic $Z^d$-actions
| dc.creator | Einsiedler, Manfred | |
| dc.creator | Lind, Douglas | |
| dc.creator | Miles, Richard | |
| dc.creator | Ward, Thomas | |
| dc.date | 2001-04-27 | |
| dc.date.accessioned | 2026-07-07T06:31:01Z | |
| dc.date.available | 2026-07-07T06:31:01Z | |
| dc.description | A general framework for investigating topological actions of $Z^d$ on compact metric spaces was proposed by Boyle and Lind in terms of expansive behavior along lower-dimensional subspaces of $R^d$. Here we completely describe this expansive behavior for the class of algebraic $Z^d$-actions given by commuting automorphisms of compact abelian groups. The description uses the logarithmic image of an algebraic variety together with a directional version of Noetherian modules over the ring of Laurent polynomials in several commuting variables. We introduce two notions of rank for topological $Z^d$-actions, and for algebraic $Z^d$-actions describe how they are related to each other and to Krull dimension. For a linear subspace of $R^d$ we define the group of points homoclinic to zero along the subspace, and prove that this group is constant within an expansive component. | |
| dc.description | 39 pages, 9 eps figures | |
| dc.identifier | https://arxiv.org/abs/math/0104261 | |
| dc.identifier | http://arxiv.org/abs/math/0104261 | |
| dc.identifier | Ergodic Theory and Dynamical Systems, 21 (2001), no. 6, 1695-1729 | |
| dc.identifier | doi:10.1017/S014338570100181X | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98496 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 22D40; 37B05 | |
| dc.title | Expansive subdynamics for algebraic $Z^d$-actions | |
| dc.type | text |