Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities
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A01=Matteo Ruggiero
A01=William Gignac
Author_Matteo Ruggiero
Author_William Gignac
Category=PBK
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Product details
- ISBN 9781470449582
- Weight: 220g
- Dimensions: 178 x 254mm
- Publication Date: 30 Mar 2022
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
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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.
William Gignac, University of Michigan, Ann Arbor, MI.
Matteo Ruggiero, University of Torino, Italy.
Matteo Ruggiero, University of Torino, Italy.
