LIMIT AVERAGE SHADOWING AND DOMINATED SPLITTING

Limit Shadowing Property

In this paper pseudoorbits of discrete dynamical systems are considered such that the one{step errors of the orbits tend to zero with increasing indices. First it is shown that close to hyperbolic sets such orbits are shadowed by true trajectories of the system with shadowing errors also tending to zero. Then the rates of convergence are studied via considering pseudoorbits such that the error ...

Pinball billiards with dominated splitting

We study the dynamics of a type of nonconservative billiards where the ball is “kicked” by the wall giving a new impulse in the direction of the normal. For different types of billiard tables we study the existence of attractors with dominated splitting.

Dominated Splitting with Stably Expansive

In this paper, we show that if a transitive set Λ is C-stably expansive, then Λ admits a dominated splitting.

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...

Dominated Splitting and Zero Volume for Incompressible Three-flows

We prove that there exists an open and dense subset of the incompressible 3-flows of class C2 such that, if a flow in this set has a positive volume regular invariant subset with dominated splitting for the linear Poincaré flow, then it must be an Anosov flow. With this result we are able to extend the dichotomies of Bochi-Mañé (see [26, 13, 9]) and of Newhouse (see [30, 10]) for flows with sin...

On ergodicity of systems with the asymptotic average shadowing property