HIDDEN SYMMETRIES AND NONLOCAL GROUP GENERATORS FOR ORDINARY DIFFERENTIAL-EQUATIONS

Hidden symmetries of ordinary differential equations (ODEs) are studie d with nonlocal group generators. General forms are given for an expon ential nonlocal group generator of an ODE that is reduced from a highe r-order ODE, which is expressed in canonical variables and which is in variant under a two-parameter Lie group. The nonlocal group generator identifies a type I hidden symmetry. Type II hidden symmetries are fou nd in some reduction pathways of an ODE invariant under a solvable, no nabelian, three-parameter Lie group. The algorithm for the appearance of the type II hidden symmetry is stated. General forms for the reduce d nonlocal group generator, which identifies the type II hidden symmet ry, are presented when the other two commuting original group generato rs are in normal form.