Abstract
We study the box geometry of bi-modal maps. As has been expected, unlike in the unimodal case, there may be non-renormalizable mappings which do not show the decay of geometry. We provide an example. On the other hand, we come up with a natural pattern in which the critical orbits are closely intertwined, but the decay of geometry persists. All this is done in the context of a generally defined box inducing construction for bi-modal maps.
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