Multiplicative Cellular Automata on Nilpotent Groups: Structure, Entropy, and Asymptotics
| dc.creator | Pivato, Marcus | |
| dc.date | 2001-08-12 | |
| dc.date | 2002-08-28 | |
| dc.date.accessioned | 2026-07-07T04:42:57Z | |
| dc.date.available | 2026-07-07T04:42:57Z | |
| dc.description | If M is a monoid (e.g. the lattice Z^D), and G is a finite (nonabelian) group, then G^M is a compact group; a `multiplicative cellular automaton' (MCA) is a continuous transformation F:G^M-->G^M which commutes with all shift maps, and where nearby coordinates are combined using the multiplication operation of G. We characterize when MCA are group endomorphisms of G^M, and show that MCA on G^M inherit a natural structure theory from the structure of G. We apply this structure theory to compute the measurable entropy of MCA, and to study convergence of initial measures to Haar measure. | |
| dc.description | LaTeX2E Format, 20 pages, 2 tables. To appear in Journal of Statistical Physics. REVISION 1: extensive notational improvement. Some results extended or improved; minor errors corrected. REVISION 2: Title changed (Old title was ``Nonabelian Multiplicative Cellular Automata''). Some proofs/examples suppressed for brevity. Some sections reorganized. Minor errors corrected | |
| dc.identifier | https://arxiv.org/abs/math/0108084 | |
| dc.identifier | http://arxiv.org/abs/math/0108084 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62008 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37B15, 68Q80 | |
| dc.title | Multiplicative Cellular Automata on Nilpotent Groups: Structure, Entropy, and Asymptotics | |
| dc.type | text |