Dynamics of certain smooth one-dimensional mappings I: The C^1+α-Denjoy-Koebe distortion lemma

1991/01/11 by Yunping Jiang, Jiang, Yunping
Engineering · Mathematics · #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.math/9201277

openalex publication_date 1991/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a technical lemma, the C^1+α-Denjoy-Koebe distortion lemma, estimating the distortion of a long composition of a C^1+α one-dimensional mapping f:M↦ M with finitely many, non-recurrent, power law critical points. The proof of this lemma combines the ideas of the distortion lemmas of Denjoy and Koebe.

Related

• One-dimensional maps and Poincaré metric
• Dynamics of certain smooth one-dimensional mappings II: geometrically finite one-dimensional mappings
• Dynamics of certain smooth one-dimensional mappings III: Scaling function geometry
• Fourier decay in parabolic C^1+α systems with overlaps
• On bounded distortions of maps in the line