Existence and Uniqueness of Orbital Measures
| dc.creator | Barnsley, Michael | |
| dc.date | 2005-07-30 | |
| dc.date.accessioned | 2026-07-07T05:22:07Z | |
| dc.date.available | 2026-07-07T05:22:07Z | |
| dc.description | We note an elementary proof of the existence and uniqueness of a solution $% μ\in \mathbb{P(X)}$ to the equation $μ=pμ_{0}+q\hat{F}μ$. Here $\mathbb{X}$ is a topological space, $\mathbb{P(X)}$ is the set of Borel measures of unit mass on $\mathbb{X}$, $μ_{0}\in $ $\mathbb{P(X)}$ is given, $p>0$, and $q\geq 0$ with $p+q=1$. The transformation $\hat{F}:% \mathbb{P(X)\to P(X)}$ is defined by $\hat{F}\upsilon =\tsum\limits_{n=1}^{N}p_{n}\upsilon \circ f_{n}^{-1}$ where $f_{n}:\mathbb{% X\to X}$ is continuous, $p_{n}>0$ for $n=1,2,...,N$, $N$ is a finite strictly positive integer, and $\tsum\limits_{n=1}^{N}p_{n}=1$. This problem occurs in connection with iterated function systems (IFS). | |
| dc.identifier | https://arxiv.org/abs/math/0508010 | |
| dc.identifier | http://arxiv.org/abs/math/0508010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75939 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 28A60 | |
| dc.title | Existence and Uniqueness of Orbital Measures | |
| dc.type | text |