{"product_id":"local-dynamics-of-non-invertible-maps-near-normal-surface-singularities","title":"Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities","description":"We study the problem of finding algebraically stable models for non-invertible holomorphic fixed point germs f : (X, x0) --\u0026gt; (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? --\u0026gt; (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 by understanding the dynamics induced by f on a space of valuations associated to X; in fact, we are able to give a strong classification of all the possible dynamical behaviors of f on this valuation space. We also deduce a precise description of the behavior of the sequence of attraction rates for the iterates of f . Finally, we prove that in this setting the first dynamical degree is always a quadratic integer.","brand":"American Mathematical Society","offers":[{"title":"Default Product","offer_id":57483989549400,"sku":"9781470449582","price":85.99,"currency_code":"EUR","in_stock":true}],"url":"https:\/\/agendabookshop.com\/products\/local-dynamics-of-non-invertible-maps-near-normal-surface-singularities","provider":"Agenda Bookshop","version":"1.0","type":"link"}