There exists a C^r diffeomorphism with a wild affine blender-horseshoe that is robustly strongly pluripotent for the majority subset but not the whole set, creating a robust obstruction to full strong pluripotency.
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A robust obstruction to full strong pluripotency for wild blender-horseshoes
There exists a C^r diffeomorphism with a wild affine blender-horseshoe that is robustly strongly pluripotent for the majority subset but not the whole set, creating a robust obstruction to full strong pluripotency.