Linearization of topologically Anosov homeomorphisms of non compact surfaces of genus zero and finite type.

We study the dynamics of topologically Anosov homeomorphisms of non-compact surfaces. In the case of surfaces of genus zero and finite type, we classify them. We prove that if f : S → S, is a Topologically Anosov homeomorphism where S is a non-compact surface of genus zero and finite type, then S = R 2 and f is conjugate to a homothety or reverse homothety (depending on wether f preserves or reverses orientation). A weaker version of this result was conjectured in [the first author et al., Topol. Methods Nonlinear Anal. 54, No. 1, 371–382 (2019; Zbl 1435.37065)]