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[null,"1.","Record Nr.",null,"UNINA9910972376703321"]
[null,null,"Autore",null,"Gignac William"]
[null,null,"Titolo",null,"Local Dynamics of Non-Invertible Maps near Normal Surface Singularities"]
[null,null,"Pubbl/distr/stampa",null,"Providence : , : American Mathematical Society, , 2021"]
[{"$nulls":4},"©2021"]
[null,null,"ISBN",null,"9781470467531"]
[{"$nulls":4},"1470467534"]
[null,null,"Edizione",null,"[1st ed.]"]
[null,null,"Descrizione fisica",null,"1 online resource (118 pages)"]
[null,null,"Collana",null,"Memoirs of the American Mathematical Society ; ; v.272"]
[null,null,"Classificazione",null,"32S0532H5013A1837P5032S45"]
[null,null,"Disciplina",null,"514/.746"]
[null,null,"Soggetti",null,"Singularities (Mathematics)"]
[{"$nulls":4},"Holomorphic mappings"]
[{"$nulls":4},"Germs (Mathematics)"]
[{"$nulls":4},"Holomorphic functions"]
[{"$nulls":4},"Several complex variables and analytic spaces -- Singularities -- Local singularities"]
[{"$nulls":4},"Several complex variables and analytic spaces -- Holomorphic mappings and correspondences -- Iteration problems"]
[{"$nulls":4},"Commutative algebra -- General commutative ring theory -- Valuations and their generalizations"]
[{"$nulls":4},"Dynamical systems and ergodic theory -- Arithmetic and non-Archimedean dynamical systems -- Dynamical systems on Berkovich spaces"]
[{"$nulls":4},"Several complex variables and analytic spaces -- Singularities -- Modifications; resolution of singularities"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references."]
[null,null,"Nota di contenuto",null,"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."]
[null,null,null,"Sommario/riassunto","\"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 "]
[{"$nulls":4},"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\"--"]