Periodic points and shadowing for generic Lebesgue measure-preserving interval maps

Abstract In this article we study dynamical behaviour of generic Lebesgue measure-preserving interval maps. We show that for each k ⩾ 1 the set periodic points period at least is a Cantor Hausdorff dimension zero and upper box one. Moreover, obtain analogous results also in context circle Furthermore, building on former results, there dense collection transitive maps whose have full measure positive 1. Finally, continuous which preserve satisfy shadowing property.