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A diffeomorphism exhibits a blender if it has an invariant hyperbolic setwith the $C^1$-robust property that its stable or unstable manifold behaves asa higher-dimensional set than is expected from the underlying hyperbolicsplitting. We present a characterisation of a blender based on the topologicalalignment of certain sets in phase space in combination with the propagation ofcones. Importantly, the required conditions can be verified by checkingproperties of a single iterate of the diffeomorphism, which is achieved byfinding finite series of sets that form suitable sequences of alignments. Thischaracterisation is applicable to blenders formed by manifolds of anydimension, in ambient phase spaces of any dimension. Moreover, this approachnaturally extends to identifying blenders that are part of heterodimensionalcycles, which provides us with the computational tool to establish theirrobustness. Our setup is flexible and allows for a rigorous, computer-assistedvalidation based on interval arithmetic. By way of demonstration, we present acomputer-assisted proof of the existence of a blender in a three-dimensionalH{\'e}non-like family of diffeomorphisms over a considerable range of therelevant parameter.

Characterising blenders via covering relations and cone conditions