Characterising blenders via covering relations and cone conditions

Abstract

We present a characterisation of a blender based on the topological alignment of certain sets in phase space in combination with cone conditions. Importantly, the required conditions can be verified by checking properties of a single iterate of the diffeomorphism, which is achieved by finding finite series of sets that form suitable sequences of alignments. This characterisation is applicable in arbitrary dimension. Moreover, the approach naturally extends to establishing $C^1$-persistent heterodimensional cycles. Our setup is flexible and allows for a rigorous, computer-assisted validation based on interval arithmetic.