Expansive partially hyperbolic diffeomorphisms with one-dimensional center (Q6583760)

Given a diffeomorphism \(f: M \to M\), which is {expansive}, {partially hyperbolic} and {dynamically coherent} with {one-dimensional center} subbundle, the authors study some sufficient conditions for \(f\) to be {(topologically) Anosov}. The conditions can be chosen among one of the following (see Theorem 1.3):\N\begin{enumerate}\N\item[(1)] \(\Omega(f) = M\); \N\item[(2)] The (topological) stable index of all the periodic points is the same;\N\item[(3)] The dimension of stable (or unstable) subbundle is one;\N\item[(4)] \(\dim M \leq 4\);\N\item[(5)] \(f\) has the pseudo-orbit tracing property (meaning that for each \(\beta > 0\), \(\exists \alpha > 0\) such that for any \(\alpha\)-pseudo orbit \(\{x_n:n \in \mathbb{Z}\}\) there is \(y \in M\) with \(\mathrm{dist}(f^n(y), x_n) < \beta\) for all \(n \in \mathbb{Z}\)).\N\end{enumerate}