Discrete integrable systems from continuous Painleve equations through limiting procedures

Based on the relation between discrete Painleve equations of difference typ e and the continuous ones we derive new discrete integrable systems. The me thod we use is to take adequate limits of the independent variable (of the continuous equation) which appears as a parameter in the discrete system. T he resulting systems are integrable and are either new (or already known) d iscrete Painleve equations or equations which are linearizable. Far the exp licit integration of some of the latter a new linearization method is intro duced. AMS classification scheme numbers: 33E17, 35Q51, 58F07.