  This work investigates topological chaos for homeomorphisms of the open
annulus, introducing a new set of sufficient conditions based on points with
distinct rotation numbers and their topological relation to invariant continua.
These conditions allow us to formulate classic methods for verifying annular
chaos in a finitely verifiable version supported on basic properties of the
map. The results pave the way for simple computer-assisted proofs of chaos in a
wide range of annular maps, including many well known examples, and we present
these proofs for some analytic families, demonstrating the effectiveness of the
method. On the theoretical side, one of the consequences of the established
conditions permits the proof of a folkloric conjecture about the relation
between topological entropy and rotation sets.
