Year: 2015
Type: preprint
Abstract: The average shadowing property is considered for set-valued dynamical systems, generated by parameterized IFS, which are uniformly contracting, or conjugacy, or products of such ones. We also prove that if a continuous surjective IFS F on a compact metric space X has the aver- age shadowing property, then every point x is chain recurrent. Moreover, we introduce some examples and investigate the relationship between the original shadowing property and shadowing property for IFS. For example, this is proved that the Sierpinski IFS has the average shadowing property. Then we shows that there is an IFS F on S1 such that F does not sat- isfy the average shadowing property but every point x in S1 is a chain recurrent.
Source: arXiv (Cornell University)
Author: Nia, Mehdi Fatehi
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1580588091