Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions: • X is a divergence-free vector field satisfying the shadowing property. • X is a divergence-free vector field satisfying the Lipschitz shadowing property. • X is an expansive divergence-free vector field. • X has no singularities a...

In this paper, we show the followings: (i) If a volume preserving diffeomorphism f belongs to the C-interior of the set of all volume preserving diffeomorphims having the ergodic shadowing property then it is transitive Anosov. Moreover, (ii) if a C-generic volume-preserving diffeomorphism f has the ergodic shadowing property then it is transitive Anosov. M.S.C. 2010: 37C50, 37D20.

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. well-posedness the problem and limit shadowing property are also discussed. Some examples given order support our results, last part considers some applications main results. first section devoted study existence a solution boundary value problem. In second section, we solutions fra...

In this paper, we introduce two new types of enriched contractions, viz., A-contraction and A-contraction. Then obtain fixed points mappings satisfying such contractions using the point property average operator mappings. Further, study well-posedness limit shadowing problem involving give some examples to validate results proved. Our work improves Berinde P?curar?s recent on different kinds we...

We prove that chaotic flows (i.e. flows that satisfy the shadowing property and have a dense subset of periodic orbits) satisfy a reparametrized gluing orbit property similar to the one introduced in [7]. In particular, these are strongly transitive in balls of uniform radius. We also prove that the shadowing property for a flow and a generic time-t map, and having a dense subset of periodic or...