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 pos...

in this paper we study shadowing property for sequences of mappings on compact metric spaces, i.e. nonautonomous discrete dynamical systems. we investigate the relation of  weak contractions with shadowing and h-shadowing property.

We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of the dynamics of center disks, is introduced. Some results on shadowing near a non-hyperbolic fixed point of a homeomorphism are obtained.

We prove that, under a mild condition on the hyperbolicity of its periodic points, a map g which is topologically conjugated to a hyperbolic map (respectively, an expanding map) is also a hyperbolic map (respectively, an expanding map). In particular, this result gives a partial positive answer for a question done by A. Katok, in a related context.

In this paper we study shadowing property for sequences of mappings on compact metric spaces, i.e. nonautonomous discrete dynamical systems. We investigate the relation of  weak contractions with shadowing and h-shadowing property.

— We consider the Klein-Gordon equation (KG) on a Riemannian surface M ∂ t u−∆u−mu+ u = 0, p ∈ N, (t, x) ∈ R×M, which is globally well-posed in the energy space. Viewed as a first order Hamiltonian system in the variables (u, v ≡ ∂tu), the associated flow lets invariant the two dimensional space of (u, v) independent of x. It turns out that in this invariant space, there is a homoclinic orbit t...

— We consider the Klein-Gordon equation (KG) on a Riemannian surface M ∂ t u−∆u−mu+ u = 0, p ∈ N, (t, x) ∈ R×M, which is globally well-posed in the energy space. Viewed as a first order Hamiltonian system in the variables (u, v ≡ ∂tu), the associated flow lets invariant the two dimensional space of (u, v) independent of x. It turns out that in this invariant space, there is a homoclinic orbit t...

In this article we approach some of the basic questions in topological dynamics, concerning periodic points, transitivity, shadowing and gluing orbit properties, context C 0 incompressible flows generated by Lipschitz vector fields. We prove that a -generic fixed-point free flow satisfies property, it is transitive has dense set points non-wandering set. particular, reparametrized property. als...

Pronunciation is essential to appropriate communication because the incorrect use ofpronunciation inevitably leads to the message being misunderstood by the receptor. In spite of itsimportance, L2 learners often regard pronunciation as the most difficult language skill to learn.In this study, shadowing as an act or task in pronunciation, in which the learner tracks the targetspeech and repeats ...