Computer-assisted proofs for blenders

A blender is a hyperbolic set whose stable, or unstable, manifold, when looking at certain intersections, appears to have a greater dimension than it actually does. In this thesis, we present a characterisation of blenders based on mapping properties of certain sets of curves that can be rigorously verified by computer-assisted methods. We develop an algorithm to construct these sets of curves that requires only a rough approximation of the strong unstable direction in a prescribed region. Since our approach does not rely on precise data, such as the exact location of invariant manifolds or fixed points, it provides a systematic framework to verify blenders in explicit examples. Here, we apply this framework to rigorously verify that a family of three-dimensional Henon-like maps presents blenders.