The Measure-Theoretical Entropy of a Linear Cellular Automata with respect to a Markov Measure
| dc.creator | Akin, Hasan | |
| dc.date | 2006-09-01 | |
| dc.date.accessioned | 2026-07-07T07:24:23Z | |
| dc.date.available | 2026-07-07T07:24:23Z | |
| dc.description | In this paper we study the measure-theoretical entropy of the one-dimensional linear cellular automata (CA hereafter) $T_{f[-l,r]}$, generated by local rule $f(x_{-l},...,x_{r})= \sum\limits_{i=-l}^{r}λ_{i}x_{i}(\text{mod}\ m)$, where $l$ and $r$ are positive integers, acting on the space of all doubly infinite sequences with values in a finite ring $\mathbb{Z}_{m}$, $m \geq 2$, with respect to a Markov measure. We prove that if the local rule $f$ is bipermutative, then the measure-theoretical entropy of linear CA $T_{f[-l,r]}$ with respect to a Markov measure $μ_{πP}$ is $ h_{μ_{πP}}(T_{f[-l,r]})=-(l+r)\sum\limits_{i,j=0}^{m-1}p_ip_{ij}\text{log} p_{ij}.$ | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/math/0609015 | |
| dc.identifier | http://arxiv.org/abs/math/0609015 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116334 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Functional Analysis | |
| dc.subject | 28D15; 37A15 | |
| dc.title | The Measure-Theoretical Entropy of a Linear Cellular Automata with respect to a Markov Measure | |
| dc.type | text |