TY - GEN

T1 - Taylor domination, difference equations, and Bautin ideals

AU - Batenkov, Dmitry

AU - Yomdin, Yosef

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2016.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Bautin ideals

KW - Domination of initial Taylor coefficients

KW - Recurrence relations

UR - http://www.scopus.com/inward/record.url?scp=84994891062&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-52927-0_21

DO - 10.1007/978-3-662-52927-0_21

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AN - SCOPUS:84994891062

SN - 9783662529263

T3 - Springer Proceedings in Mathematics and Statistics

SP - 303

EP - 319

BT - Difference Equations, Discrete Dynamical Systems and Applications - ICDEA 2012

A2 - Cushing, Jim M.

A2 - Pinto, Alberto A.

A2 - Elaydi, Saber

A2 - i Soler, Lluis Alseda

PB - Springer New York LLC

T2 - 18th International Conference on Difference Equations and Applications, ICDEA 2012

Y2 - 23 July 2012 through 27 July 2012

ER -