One class of structurally stable endomorphisms on an infinite-dimensional torus (Q2212366)

Let \({\mathbb T}^\infty\) be an infinite-dimensional torus, that is, the quotient space of some Banach space by an integer lattice. For an arbitrary expanding endomorphism of \(C^1\)-class acting from \({\mathbb T}^\infty\) to itself, the authors establish some standard assertions from the hyperbolic theory: 1) this endomorphism is topologically conjugate to a linear endomorphism of the torus; 2) this endomorphism is \(C^1\)-strong structural stable, and 3) if the fundamental set of \({\mathbb T}^\infty\) is bounded, then each expanding endomorphism of this torus is topologically mixing.