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Eigenvaluations
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). University of Michigan, United States .
2007 (English)In: Annales Scientifiques de l'Ecole Normale Supérieure, ISSN 0012-9593, E-ISSN 1873-2151, Vol. 40, no 2, 309-349 p.Article in journal (Refereed) Published
Abstract [en]

We study the dynamics in C-2 of superattracting fixed point germs and of polynomial maps near infinity. In both cases we show that the asymptotic attraction rate is a quadratic integer, and construct a plurisubharmonic function with the adequate invariance property. This is done by finding an infinitely near point at which the map becomes rigid: the critical set is contained in a totally invariant set with normal crossings. We locate this infinitely near point through the induced action of the dynamics on a space of valuations. This space carries an R-tree structure and conveniently encodes local data: an infinitely near point corresponds to an open subset of the tree. The action respects the tree structure and admits a fixed point-or eigenvaluation-which is attracting in a certain sense. A suitable basin of attraction corresponds to the desired infinitely near point.

Place, publisher, year, edition, pages
2007. Vol. 40, no 2, 309-349 p.
Keyword [en]
polynomial-mappings, rational mappings, one place, dynamics, infinity, curves, maps, surfaces, space, c-2
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-16829DOI: 10.1016/j.ansens.2007.01.002ISI: 000248409200004Scopus ID: 2-s2.0-34347354409OAI: oai:DiVA.org:kth-16829DiVA: diva2:334872
Note

QC 20100525

Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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