Abstract
Given a nonempty compact metric space X and a continuous
function f : X → X, we study shadowing and h-shadowing for
the induced maps on hyperspaces, particularly in symmetric products,
Fn(X), and the hyperspace of compact subsets of X, 2X. We prove
that f has shadowing (h-shadowing) if and only if 2f has shadowing
(h-shadowing).
function f : X → X, we study shadowing and h-shadowing for
the induced maps on hyperspaces, particularly in symmetric products,
Fn(X), and the hyperspace of compact subsets of X, 2X. We prove
that f has shadowing (h-shadowing) if and only if 2f has shadowing
(h-shadowing).
| Original language | English |
|---|---|
| Pages (from-to) | 277-286 |
| Number of pages | 10 |
| Journal | Fundamenta Mathematicae |
| Volume | 235 |
| Early online date | 4 Jul 2016 |
| DOIs | |
| Publication status | Published - 2016 |
Keywords
- shadowing
- pseudo orbit tracing
- induced map
- hyperspace