Analysis of spurious synchronization with positive conditional Lyapunov exponents in computer simulations (Q1961667)

This paper deals with partially hyperbolic diffeomorphisms preserving a splitting of the tangent bundle into a strong-unstable subbundle \(E^{\text{un}}\) (uniformly expanding) and a subbundle \(E^c\), dominated by \(E^{\text{un}}\). They show that if the central direction \(E^c\) is mostly contracting for the diffeomorphism, then the ergodic Gibbs \(u\)-states are the SRB measures, there are finitely many of them, and their basins cover a full measure subset. Moreover, they prove that if the strong-unstable leaves are dense, then there is a unique SRB measure. The authors also provide some applications of the results mentioned above.