Local Dynamics of Non-invertible Maps Near Normal Surface Singularities (Memoirs of the American Mathematical Society, 272) - Softcover

Gignac, William ; Ruggiero, Matteo

9781470449582: Local Dynamics of Non-invertible Maps Near Normal Surface Singularities (Memoirs of the American Mathematical Society, 272)

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ISBN 10: 1470449587 ISBN 13: 9781470449582

Verlag: American Mathematical Society, 2021

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Gignac and Ruggiero study the problem of finding algebraically stable models for non-invertible holomorphic fixed point germs f: (X,x0) to (X,x0), where X is a complex surface having x0 as a normal singularity. Their topics include normal surface singularities and their valuation spaces, dynamics on valuation spaces, dynamics of non-invertible finite germs, algebraic stability, attraction rates, and examples and remarks. Annotation �2022 Ringgold, Inc., Portland, OR (protoview.com)

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�ber die Autorin bzw. den Autor

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

Matteo Ruggiero, University of Torino, Italy.

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Verlag: American Mathematical Society
Erscheinungsdatum: 2021
Sprache: Englisch
ISBN 10: 1470449587
ISBN 13: 9781470449582
Einband: Taschenbuch
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Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities

William Gignac

Verlag: MP-AMM American Mathematical, 2022

ISBN 10: 1470449587 ISBN 13: 9781470449582

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Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities

William Gignac, Matteo Ruggiero

Verlag: American Mathematical Society, US, 2022

ISBN 10: 1470449587 ISBN 13: 9781470449582

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Paperback. Zustand: 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. Bestandsnummer des Verk�ufers LU-9781470449582

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