By using the cycle expansion, we obtain general expressions for the determination of the diffusion coefficient D of a piecewise linear map which is parametrized by k and h-tilde (where the map contains 2k+5 branches of line segment, and h-tilde is the height of the shortest line). By restricting h-tilde= beta /m [ beta =1,...,(k+1)/2; m is the slope of the map], a closed form expression of D can be obtained and some of its consequences are discussed. The limiting form of D (k--> [infinity] ) is then shown to be k2. For the simplest case with k=1, we also show that more exact results can be found. A limiting case with h-tilde-->0 is discussed where agreement with the result obtained from the invariant measure approach is established.
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