| | |
| | |
Stat |
Members: 3645 Articles: 2'500'096 Articles rated: 2609
19 April 2024 |
|
| | | |
|
Article overview
| |
|
Selections and their Absolutely Continuous Invariant Measures | A. Boyarsky
; P. Góra
; Zh. Li
; | Date: |
24 Sep 2013 | Abstract: | Let $I=[0,1]$ and consider disjoint closed regions $G_{1},....,G_{n}$ in $%
I imes I$ and subintervals $I_{1},......,I_{n},$ such that $G_{i}$ projects
onto $I_{i.}$ We define the lower and upper maps $ au_{1},$ $ au_{2}$ by the
lower and upper boundaries of $G_{i},i=1,....,n,$ respectively. We assume
$ au_{1}$, $ au_{2}$ to be piecewise monotonic and preserving continuous
invariant measures $mu_{1}$ and $mu_{2}$, respectively. Let $% F^{(1)}$ and
$F^{(2)}$ be the distribution functions of $mu_{1}$ and $mu_{2}.$ The main
results shows that for any convex combination $F$ of $% F^{(1)} $ and $F^{(2)}$
we can find a map $eta $ with values between the graphs of $ au_{1}$ and
$ au_{2}$ (that is, a selection) such that $F$ is the $eta $-invariant
distribution function. Examples are presented. We also study the relationship
of the dynamics of multi-valued maps to random maps. | Source: | arXiv, 1309.6009 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |