Multi-sensitivity, syndetical sensitivity and the asymptotic average- shadowing property for continuous semi-flows

The sequence asymptotic average shadowing property and transitivity

Let X be a compact metric space and f be a continuous map from X into itself. In this paper, we introduce the concept of the sequence asymptotic average shadowing property, which is a generalization of the asymptotic average shadowing property. In the sequel, we prove some properties of the sequence asymptotic average shadowing property and investigate the relationship between the sequence asym...

On ergodicity of systems with the asymptotic average shadowing property

Continuous and Inverse Shadowing for Flows

We define continuous and inverse shadowing for flows and prove some properties. In particular, we will prove that an expansive flow without fixed points on a compact metric space which is a shadowing is also a continuous shadowing and hence an inverse shadowing (on a compact manifold without boundary).

Shadowing Property of Continuous Maps

We study continuous maps of an interval into itself. We find the necessary and sufficient condition for the maps of the type 2" to have the shadowing property. Further we show that any chaotic map, which has only cycles of order a power of 2, does not have the shadowing property. Introduction Let /:/(=(0;l))—»7 be a continuous map of the interval 7 to itself (i.e., / G C°(7, 7)). The orbit of x...

THE CHAIN PROPERTIES AND LI-YORKE SENSITIVITY OF ZADEH'S EXTENSION ON THE SPACE OF UPPER SEMI-CONTINUOUS FUZZY SETS

Some characterizations on the chain recurrence, chain transitivity, chain mixing property,shadowing and $h$-shadowing for Zadeh's extension are obtained. Besides, it is provedthat a dynamical system is spatiotemporally chaotic provided that the Zadeh's extensionis Li-Yorke sensitive.