Dynamics of infinite-multivalued transformations
| dc.creator | Igudesman, Konstantin | |
| dc.date | 2004-12-08 | |
| dc.date.accessioned | 2026-07-07T05:15:04Z | |
| dc.date.available | 2026-07-07T05:15:04Z | |
| dc.description | We consider a transformation of a normalized measure space such that the image of any point is a finite set. We call such transformation $m$-transformation. In this case the orbit of any point looks like a tree. In the study of $m$-transformations we are interested in the properties of the trees. An $m$-transformation generates a stochastic kernel and a new measure. Using these objects, we introduce analogies of some main concept of ergodic theory: ergodicity, Koopman and Frobenius-Perron operators etc. We prove ergodic theorems and consider examples. We also indicate possible applications to fractal geometry and give a generalization of our construction. Some results which have analogies in the classical ergodic theory we are proved using standard methods. Other results have no analogies. | |
| dc.description | 16 pages, latex | |
| dc.identifier | https://arxiv.org/abs/math/0412158 | |
| dc.identifier | http://arxiv.org/abs/math/0412158 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73517 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37A05; 28D05; 28A80 | |
| dc.title | Dynamics of infinite-multivalued transformations | |
| dc.type | text |