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

William Gignac (author) & Matteo Ruggiero (author)

Softcover

ISBN 10: 1470449587 ISBN 13: 9781470449582

Publisher: American Mathematical Society, 2022

Synopsis

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.

About this title

About the Author

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

Matteo Ruggiero, University of Torino, Italy.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2022
• Language: English
• ISBN 10: 1470449587
• ISBN 13: 9781470449582
• Binding: Paperback
• Number of pages: 277