Local dynamics of non-invertible maps near normal surface singularities
著者
書誌事項
Local dynamics of non-invertible maps near normal surface singularities
（Memoirs of the American Mathematical Society, no. 1337）
American Mathematical Society, c2021
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注記
"July 2021, volume 272, number 1337 (seventh of 7 numbers)"
Includes bibliographical references (p. 97-100)
内容説明・目次
内容説明
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.
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