Towards the complete classification of generalized tent maps inverse limits

We study generalized tent maps inverse limits, i.e. inverse limits of inverse sequences of unit segments I with a generalized tent map being the only bonding function. As the main result we identify an infinite family of curves in I 2 such that if top points of graphs of generalized tent maps belong to the same curve, the corresponding inverse limits are homeomorphic, and if they belong to different curves, the inverse limits are non-homeomorphic. The inverse limits corresponding to certain families of top points are explicitly determined, and certain properties of the inverse limit are proved in the case of ( 0 , 1 ) as the top point.