Taylor domination, difference equations, and Bautin ideals

Dmitry Batenkov, Yosef Yomdin

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


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
Number of pages17
StatePublished - 2016
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


Conference18th International Conference on Difference Equations and Applications, ICDEA 2012


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

All Science Journal Classification (ASJC) codes

  • General Mathematics


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