Local Dynamics of Non-Invertible Maps near Normal Surface Singularities

• Autore: Gignac William
• Pubblicazione: Providence : , : American Mathematical Society, , 2021; ©2021
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (118 pages)
• Disciplina: 514/.746
• Soggetto topico: Singularities (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
• Classificazione: 32S0532H5013A1837P5032S45
• Altri autori: RuggieroMatteo
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: 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.
• 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 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"--
• Titolo autorizzato: Local Dynamics of Non-Invertible Maps near Normal Surface Singularities
• ISBN: 9781470467531; 1470467534
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910972376703321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society