Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities Andrea J. (Jo) Stairs The latter part of the

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Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities Andrea J. (Jo) Stairs The latter part of theWe study the problem of finding algebraically stable models for non invertible holomorphic fixed point germs f : (X, x0) > (X, x0), where X is a complex surface having x0 as a normal singularity. We prove that as long as x0 is not a cusp singularity of X, then it is possible to find arbitrarily high modifications ?: X? > (X, x0) such that the dynamics of f (or more precisely of fN for N big enough) on X? is algebraically stable. This result is proved