Stable transitivity for extensions of hyperbolic systems by semidirect products of compact and nilpotent Lie groups (Q632363)

Let \(X\) be a hyperbolic basic set. The \(G\)-extension \(f_\beta\) is called transitive, if it has a forward dense orbit. The problem of interest of the paper is whether non-compact Lie group extensions of a hyperbolic basic set are typically stably topologically transitive. The conjecture for the case when the fiber \(G\) is an extension of a nilpotent Lie group by a compact semi-simple Lie group is studied.