S-limit shadowing is generic for continuous Lebesgue measure preserving circle maps

TL;DR

This paper proves that the s-limit shadowing property is generic among continuous Lebesgue measure preserving circle maps and extends this to all continuous circle maps, implying several shadowing properties are also generic.

Contribution

It establishes the genericity of s-limit shadowing for both Lebesgue measure preserving and general continuous circle maps, unifying shadowing properties in these settings.

Findings

s-limit shadowing is generic for Lebesgue measure preserving circle maps

s-limit shadowing is generic for all continuous circle maps

classical, periodic, and limit shadowing are also generic in these contexts

Abstract

In this paper we show that generic continuous Lebesgue measure preserving circle maps have the s-limit shadowing property. In addition we obtain that s-limit shadowing is a generic property also for continuous circle maps. In particular, this implies that classical shadowing, periodic shadowing and limit shadowing are generic in these two settings as well.