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Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities (Memoirs of the American Mathematical Society, 272) - Softcover
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William Gignac, and Matteo Ruggiero, Université de Paris and Sorbonne Université, France
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Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities
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American Mathematical Society, US, 2022
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Paperback. Condition: New. 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. Seller Inventory # LU-9781470449582
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Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities
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Local Dynamics of Non-invertible Maps Near Normal Surface Singularities: July 2021; Number 1337 (Seventh of 7 Numbers)
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Local Dynamics Of Non-invertible Maps Ne
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ISBN 13: 9781470449582
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Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities
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American Mathematical Society, 2021
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ISBN 13: 9781470449582
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Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities
Published by
American Mathematical Society, US, 2022
ISBN 10: 1470449587
ISBN 13: 9781470449582
New
Paperback
Seller: Rarewaves.com UK, London, United Kingdom
Seller rating 5 out of 5 stars
Paperback. Condition: New. 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. Seller Inventory # LU-9781470449582
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