On the Poincar\'{e} functional equation
Sergei Kazenas
TL;DR
This paper presents a formula for solving the Poincaré functional equation within formal power series algebra and explores its application to continuous iteration processes.
Contribution
It introduces a novel formula for the Poincaré functional equation and applies it to continuous iteration, advancing the theoretical understanding.
Findings
Derived a new solution formula for the Poincaré functional equation
Applied the formula to continuous iteration problems
Enhanced methods for solving functional equations in formal power series
Abstract
In this paper, a formula for the solution of the Poincar\'{e} functional equation in algebra of formal power series and its application to continuous iteration are presented.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFunctional Equations Stability Results · Advanced Topics in Algebra · Polynomial and algebraic computation