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TY - CONF AU - Balandin, V. AU - Golubeva, N. ED - Petit-Jean-Genaz, Christine ED - Arduini, Gianluigi ED - Michel, Peter ED - Schaa, Volker RW TI - Dynamics of Twiss Parameters from the Geometrical Viewpoint J2 - Proc. of IPAC2014, Dresden, Germany, June 15-20, 2014 C1 - Dresden, Germany T2 - International Particle Accelerator Conference T3 - 5 LA - english AB - We show that with an appropriate parametrization the linear transport of the Twiss parameters can be viewed as a bilinear (or Moebius) map of the upper complex half-plane (which is the hyperbolic plane) into itself. Using then elementary techniques of hyperbolic geometry we classify transformations of the Twiss parameters into elliptic, hyperbolic and parabolic types and, for each type, present its typical phase space portraits. PB - JACoW CP - Geneva, Switzerland SP - 1135 EP - 1137 KW - emittance KW - framework KW - betatron KW - survey DA - 2014/07 PY - 2014 SN - 978-3-95450-132-8 DO - 10.18429/JACoW-IPAC2014-TUPRO048 UR - http://jacow.org/ipac2014/papers/tupro048.pdf ER -