Local Dynamics of Non-Invertible Maps near Normal Surface Singularities.

Format:

Book

Author/Creator:

Gignac, William.

Contributor:

Ruggiero, Matteo.

Series:

Memoirs of the American Mathematical Society

Memoirs of the American Mathematical Society ; v.272

Language:

English

Subjects (All):

Singularities (Mathematics).

Holomorphic mappings.

Germs (Mathematics).

Holomorphic functions.

Physical Description:

1 online resource (118 pages)

Edition:

1st ed.

Place of Publication:

Providence : American Mathematical Society, 2021.

Summary:

"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.

Contents:

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.

Notes:

Description based on publisher supplied metadata and other sources.

Includes bibliographical references.

ISBN:

9781470467531

1470467534

OCLC:

1275392913