{"product_id":"9781470449582","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":"William Gignac","offers":[{"title":"Default Title","offer_id":46776617435454,"sku":"9781470449582","price":0.0,"currency_code":"ZAR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/products\/9781470449582_9b3f2ce7-297a-440b-ab0d-ad56b42cbfad.jpg?v=1707476999","url":"https:\/\/exclusivebooks.co.za\/products\/9781470449582","provider":"Exclusive Books Online","version":"1.0","type":"link"}