Existence and Uniqueness of Orbital Measures

Details Existence and Uniqueness of Orbital Measures Existence and Uniqueness of Orbital Measures

2005-07-30

arxiv.org/abs/math/0508010v1

Mathematics

Dynamical Systems

Scientific paper

We note an elementary proof of the existence and uniqueness of a solution $% \mu \in \mathbb{P(X)}$ to the equation $\mu =p\mu_{0}+q\hat{F}\mu $. Here $\mathbb{X}$ is a topological space, $\mathbb{P(X)}$ is the set of Borel measures of unit mass on $\mathbb{X}$, $\mu_{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).

Affiliated with

Also associated with

No associations

Rating

Existence and Uniqueness of Orbital Measures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Existence and Uniqueness of Orbital Measures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Existence and Uniqueness of Orbital Measures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-723369