  Reconnection processes of twin-chains are systematically studied in the
quadratic twist map. By using the reversibility and symmetry of the mapping,
the location of the indicator points is theoretically determined in the phase
space. The indicator points enable us to obtain useful information about the
reconnection processes and the transition to global chaos. We succeed in
deriving the general conditions for the reconnection thresholds. In addition, a
new type of reconnection process which generates shearless curves is studied.
