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Local Dynamics of Non-invertible Maps Near Normal Surface Singularities - Couverture souple

Gignac, William; Ruggiero, Matteo

 
9781470449582: Local Dynamics of Non-invertible Maps Near Normal Surface Singularities
Couverture souple
ISBN 10 : 1470449587 ISBN 13 : 9781470449582
Editeur : American Mathematical Society, 2022

Synopsis

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 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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l'auteur

William Gignac, University of Michigan, Ann Arbor, MI.

Matteo Ruggiero, University of Torino, Italy.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2022
Langue
anglais
ISBN 10 
1470449587
ISBN 13 
9781470449582
Reliure
Broché
Nombre de pages
277
Coordonnées du fabricant
non disponible
Personne responsable
non disponible