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DCDS

In this paper, we prove that stable ergodicity is $C^1$-dense among
conservative partially hyperbolic systems which, in a stable way,
have two ergodic measures
such that one has all center Lyapunov exponents non-negative and
the other one has all center Lyapunov exponents non-positive.

DCDS

In this paper, we study the limit quasi-shadowing property for diffeomorphisms. We prove that any quasi-partially hyperbolic pseudoorbit $\{x_{i},n_{i}\}_{i∈ \mathbb{Z}}$ can be $\mathcal{L}^p$-, limit and asymptotic quasi-shadowed by a points sequence $\{y_{k}\}_{k∈ \mathbb{Z}}$. We also investigate the $\mathcal{L}^p$-, limit and asymptotic quasi-shadowing properties for partially hyperbolic diffeomorphisms which are dynamically coherent.

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