Taylor domination, difference equations, and Bautin ideals

Dmitry Batenkov, Yosef Yomdin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We compare three approaches to studying the behavior of an analytic function f (z) = [formula presented] from its Taylor coefficients. The first is “Taylor domination” property for f (z) in the complex disk DR, which is an inequality of the form [formula presented]. The second approach is based on a possibility to generate ak via recurrence relations. Specifically, we consider linear non-stationary recurrences of the form [formula presented], …, with uniformly bounded coefficients. In the third approachweassume that ak = ak(λ) are polynomials in a finite-dimensional parameter λ ∈ ℂn.We study “Bautin ideals” Ik generated by a1(λ), …, ak(λ) in the ring ℂ [λ] of polynomials in λ. These three approaches turn out to be closely related. We present some results and questions in this direction.

Original languageEnglish
Title of host publicationDifference Equations, Discrete Dynamical Systems and Applications - ICDEA 2012
EditorsJim M. Cushing, Alberto A. Pinto, Saber Elaydi, Lluis Alseda i Soler
PublisherSpringer New York LLC
Pages303-319
Number of pages17
ISBN (Print)9783662529263
DOIs
StatePublished - 2016
Externally publishedYes
Event18th International Conference on Difference Equations and Applications, ICDEA 2012 - Barcelona, Spain
Duration: 23 Jul 201227 Jul 2012

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume180
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference18th International Conference on Difference Equations and Applications, ICDEA 2012
Country/TerritorySpain
CityBarcelona
Period23/07/1227/07/12

Keywords

  • Bautin ideals
  • Domination of initial Taylor coefficients
  • Recurrence relations

Fingerprint

Dive into the research topics of 'Taylor domination, difference equations, and Bautin ideals'. Together they form a unique fingerprint.

Cite this