  We reduce the earlier known optimal shear parameter for which ergodicity is
established in the linked twist map with two linear shears in opposite sense,
in the most general setting. Further, here we obtain ergodicity with possibly
only one-fold twists in either lobe, while earlier results only applied for
twist parameters at least 2. Almost hyperbolicity is easily established for
shear parameters greater than 2, while in the most general setting of the
linked twist map with both shears of equal magnitude, ergodicity was earlier
established in the most general setting by Przytycki for shear parameters
greater than 4.15 with at least two-fold twists in each lobe. Here we reduce
this optimal shear parameter to 3.47 in the general setting. These techniques
can be effected to make further improvements when additional assumptions are
made on the dimensions of the strips or when the linked twist map is modified
in other natural ways.
