Dynamics of piecewise linear maps and sets of nonnegative matrices
| dc.creator | Bondarenko, Ievgen | |
| dc.date | 2006-06-02 | |
| dc.date | 2008-09-13 | |
| dc.date.accessioned | 2026-07-07T10:02:36Z | |
| dc.date.available | 2026-07-07T10:02:36Z | |
| dc.description | We consider functions $f(v)=\min_{A\in K}{Av}$ and $g(v)=\max_{A\in K}{Av}$, where $K$ is a finite set of nonnegative matrices and by "min" and "max" we mean coordinate-wise minimum and maximum. We transfer known results about properties of $g$ to $f$. In particular we show existence of nonnegative generalized eigenvectors for $f$, give necessary and sufficient conditions for existence of strictly positive eigenvector for $f$, study dynamics of $f$ on the positive cone. We show the existence and construct matrices $A$ and $B$, possibly not in $K$, such that $f^n(v)\sim A^nv$ and $g^n(v)\sim B^nv$ for any strictly positive vector $v$. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0606047 | |
| dc.identifier | http://arxiv.org/abs/math/0606047 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169032 | |
| dc.subject | Optimization and Control | |
| dc.subject | Dynamical Systems | |
| dc.subject | 47J10 (Primary) 15A48; 15A18; 37N40 (Secondary) | |
| dc.title | Dynamics of piecewise linear maps and sets of nonnegative matrices | |
| dc.type | text |