04335nam 22007213 450 991097237670332120231110215751.097814704675311470467534(CKB)4940000000616249(MiAaPQ)EBC6798074(Au-PeEL)EBL6798074(RPAM)22490941(PPN)259967939(OCoLC)1275392913(EXLCZ)99494000000061624920211214d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierLocal Dynamics of Non-Invertible Maps near Normal Surface Singularities1st ed.Providence :American Mathematical Society,2021.©2021.1 online resource (118 pages)Memoirs of the American Mathematical Society ;v.2729781470449582 1470449587 Includes bibliographical references.Normal 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."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"--Provided by publisher.Memoirs of the American Mathematical Society Singularities (Mathematics)Holomorphic mappingsGerms (Mathematics)Holomorphic functionsSeveral complex variables and analytic spaces -- Singularities -- Local singularitiesmscSeveral complex variables and analytic spaces -- Holomorphic mappings and correspondences -- Iteration problemsmscCommutative algebra -- General commutative ring theory -- Valuations and their generalizationsmscDynamical systems and ergodic theory -- Arithmetic and non-Archimedean dynamical systems -- Dynamical systems on Berkovich spacesmscSeveral complex variables and analytic spaces -- Singularities -- Modifications; resolution of singularitiesmscSingularities (Mathematics)Holomorphic mappings.Germs (Mathematics)Holomorphic functions.Several complex variables and analytic spaces -- Singularities -- Local singularities.Several complex variables and analytic spaces -- Holomorphic mappings and correspondences -- Iteration problems.Commutative algebra -- General commutative ring theory -- Valuations and their generalizations.Dynamical systems and ergodic theory -- Arithmetic and non-Archimedean dynamical systems -- Dynamical systems on Berkovich spaces.Several complex variables and analytic spaces -- Singularities -- Modifications; resolution of singularities.514/.74632S0532H5013A1837P5032S45mscGignac William1802013Ruggiero Matteo755730MiAaPQMiAaPQMiAaPQBOOK9910972376703321Local Dynamics of Non-Invertible Maps near Normal Surface Singularities4347518UNINA