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

Gignac, William; Ruggiero, Matteo

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.

A propos du livre

À propos de l?auteur

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

Matteo Ruggiero, University of Torino, Italy.

Détails de l'édition

• 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