Continuum-wise hyperbolicity is exactly the pseudo-Anosov dynamics with spine singularities
Year: 2026
Type: preprint
Abstract: We establish a complete structural classification for cw$_F$-hyperbolic surface homeomorphisms. Specifically, we prove that a surface homeomorphism is cw$_F$-hyperbolic if, and only if, it is a pseudo-Anosov homeomorphism whose singularities consist exclusively of spines (1-prongs). Furthermore, we classify these systems up to topological conjugacy, showing that every such homeomorphism is conjugate to either an Anosov automorphism on the torus $\mathbb{T}^2$ or to a standard hyperelliptic quotient on $\mathbb{S}^2$ of a hyperbolic affine toral map. As a rigid consequence of this classification, we show that such dynamics are strictly obstructed on surfaces of genus greater than one, the Klein bottle, and the projective plane.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G3571952387
OpenAlex ID: W7164380718