E-resources
Peer reviewed
-
Ren, Rufei
Advances in mathematics (New York. 1965), 03/2023, Volume: 416Journal Article
In 7, Herman and Yoccoz prove that for any given locally analytic (at z=0) power series f(z)=z(λ+∑i=1∞aizi) over a complete non-Archimedean field of characteristic 0 if |λ|=1 and λ is not a root of unity, then f is locally linearizable at z=0. They ask the same question for power series over fields of positive characteristic. In this paper, we prove that, on opposite, most such power series in this case are more likely to be non-linearizable. More precisely, given a complete non-Archimedean field K of positive characteristic and a power series f(z)=z(λ+∑i=1∞aizi)∈K〚z〛 with λ not a root of unity and |1−λ|<1, we prove a sufficient condition (Criterion ★) for f to be non-linearizable. This phenomenon of prevalence for power series over fields of positive characteristic being non-linearizable was initially conjectured in 6, p 147 by Herman, and formulated into a concrete question by Lindahl as 9, Conjecture 2.2. As applications of Criterion ★, we prove the non-linearizability of three families of polynomials.
Author
![loading ... loading ...](themes/default/img/ajax-loading.gif)
Shelf entry
Permalink
- URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year | Impact factor | Edition | Category | Classification | ||||
---|---|---|---|---|---|---|---|---|
JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
Select the library membership card:
If the library membership card is not in the list,
add a new one.
DRS, in which the journal is indexed
Database name | Field | Year |
---|
Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
---|
Source: Personal bibliographies
and: SICRIS
The material is available in full text. If you wish to order the material anyway, click the Continue button.