Cyclic Phenomena for Composition Operators.

Intro -- Contents -- Introduction -- Cyclicity -- Cyclicity and Iteration -- Linear-Fractional" Classification of Arbitrary Maps -- Transference -- The Intertwining Map σ -- 1 Preliminaries -- The Space H[sup(2)] -- Angular Derivatives -- Cyclicity and Univalence -- Hypercyclicity Basics -- 2 Linear-Fractional Composition Operators -- Linear-Fractional Basics -- Cyclicity: First Observations -- The Main Theorem -- Remarks on "Extreme Behavior -- 3 Linear-Fractional Models -- First Applications of Transference -- Cyclicity and Fixed-Point Position -- 4 The Hyperbolic and Parabolic Models -- Expansions About the Denjoy-Wolff Point -- Consequences for Parabolic Type -- The Hyperbolic Case -- The Parabolic Case -- Consequences of The Parabolic Models Theorem -- Motivation for the Proof -- Estimates on Orbit Magnitudes -- Proof of the Parabolic Models Theorem -- 5 Cyclicity: Parabolic Nonautomorphism Case -- Applying the Parabolic Model -- A Cyclic Vector for C[sub(α)] -- 6 Endnotes -- Orbit Separation and Parabolic Subtype -- Less Differentiability -- Further Directions -- Acknowledgment -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.