LEADER 04335nam 22007213 450 001 9910972376703321 005 20231110215751.0 010 $a9781470467531 010 $a1470467534 035 $a(CKB)4940000000616249 035 $a(MiAaPQ)EBC6798074 035 $a(Au-PeEL)EBL6798074 035 $a(RPAM)22490941 035 $a(PPN)259967939 035 $a(OCoLC)1275392913 035 $a(EXLCZ)994940000000616249 100 $a20211214d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLocal Dynamics of Non-Invertible Maps near Normal Surface Singularities 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2021. 210 4$dİ2021. 215 $a1 online resource (118 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.272 311 08$a9781470449582 311 08$a1470449587 320 $aIncludes bibliographical references. 327 $aNormal surface singularities, resolutions, and intersection theory -- Normal surface singularities and their valuation spaces -- Log discrepancy, essential skeleta, and special singularities -- Dynamics on valuation spaces -- Dynamics of non-finite germs -- Dynamics of non-invertible finite germs -- Algebraic stability -- Attraction rates -- Examples and remarks. 330 $a"We study the problem of finding algebraically stable models for non-invertible holomorphic fixed point germs f : (X, x0) (X, x0), where X is a complex surface having x0 as a normal singularity. We prove that as long as x0 is not a cusp singularity of X, then it is possible to find arbitrarily high modifications : X (X, x0) such that the dynamics of f (or more precisely of f N for N big enough) on X is algebraically stable. This result is proved by understanding the dynamics induced by f on a space of valuations associated to X; in fact, we are able to give a strong classification of all the possible dynamical behaviors of f on this valuation space. We also deduce a precise description of the behavior of the sequence of attraction rates for the iterates of f . Finally, we prove that in this setting the first dynamical degree is always a quadratic integer"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aSingularities (Mathematics) 606 $aHolomorphic mappings 606 $aGerms (Mathematics) 606 $aHolomorphic functions 606 $aSeveral complex variables and analytic spaces -- Singularities -- Local singularities$2msc 606 $aSeveral complex variables and analytic spaces -- Holomorphic mappings and correspondences -- Iteration problems$2msc 606 $aCommutative algebra -- General commutative ring theory -- Valuations and their generalizations$2msc 606 $aDynamical systems and ergodic theory -- Arithmetic and non-Archimedean dynamical systems -- Dynamical systems on Berkovich spaces$2msc 606 $aSeveral complex variables and analytic spaces -- Singularities -- Modifications; resolution of singularities$2msc 615 0$aSingularities (Mathematics) 615 0$aHolomorphic mappings. 615 0$aGerms (Mathematics) 615 0$aHolomorphic functions. 615 7$aSeveral complex variables and analytic spaces -- Singularities -- Local singularities. 615 7$aSeveral complex variables and analytic spaces -- Holomorphic mappings and correspondences -- Iteration problems. 615 7$aCommutative algebra -- General commutative ring theory -- Valuations and their generalizations. 615 7$aDynamical systems and ergodic theory -- Arithmetic and non-Archimedean dynamical systems -- Dynamical systems on Berkovich spaces. 615 7$aSeveral complex variables and analytic spaces -- Singularities -- Modifications; resolution of singularities. 676 $a514/.746 686 $a32S05$a32H50$a13A18$a37P50$a32S45$2msc 700 $aGignac$b William$01802013 701 $aRuggiero$b Matteo$0755730 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910972376703321 996 $aLocal Dynamics of Non-Invertible Maps near Normal Surface Singularities$94347518 997 $aUNINA