is a hyperbola, if u = rx and v = y/r, then uv = xy and the points of the image of the squeeze mapping are on the same hyperbola as (x,y) is. For this reason it is natural to think of the squeeze mapping as a "hyperbolic rotation", as did Émile Borel in 1913.
If r and s are positive real numbers, the composition of their squeeze mappings is the squeeze mapping of their product. Therefore the collection of squeeze mappings forms a one-parameter group isomorphic to the multiplicative group of positive real numbers.An additive view of this group arises from consideration of hyperbolic sectors and hyperbolic angles.
Cognitive Mapping may be used for a variety of purposes although a "problem" of some sort usually forms the focus of the work.
Mapping is intended to impose an "action oriented perspective" onto the concept thus making it something that the problem owner can go and do as a possible part of the solution to the problem.
Thus the action orientation of mapping is as much as a way of interpreting, firstly the raw data, and secondly the map itself as an explicit modelling technique to be followed with care.
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