Universal measure for Poncelet-type theorems
  We give a simple proof of the Emch closing theorem by introducing a new invariant measure on the circle. Special cases of that measures are well-known and have been used in the literature to prove Poncelet's and Zigzag theorems. Some further generalizations are also obtained by applying the new measure. 
Evgeny A. Avksentyev, Vladimir Yu. Protasov
math.DS math.DG