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标题：Generic Properties of Koopman Eigenfunctions for Stable Fixed Points and Periodic Orbits ⁎ ⁎
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作者：Matthew D. Kvalheim ; David Hong ; Shai Revzen 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2021
卷号：54
期号：9
页码：267-272
DOI：10.1016/j.ifacol.2021.06.150
语种：English
出版社：Elsevier
摘要：AbstractOur recent work established existence and uniqueness results forCk(actually Ck,αloc)linearizing semiconjugacies forCflows defined on the entire basin of an attracting hyperbolic fixed point or periodic orbit (Kvalheim and Revzen, 2019). Applications include (i) improvements, such as uniqueness statements, for the Sternberg linearization and Floquet normal form theorems, and (ii) results concerning the existence, uniqueness, classification, and convergence of various quantities appearing in the “applied Koopmanism” literature, such as principal eigenfunctions, isostables, and Laplace averages.In this work we consider the broadness of applicability of these results with an emphasis on the Koopmanism applications. In particular we show that, for the flows of “typical” c∞vector fields having an attracting hyperbolic fixed point or periodic orbit with a fixed basin of attraction, the c∞Koopman eigenfunctions can be completely classified, generalizing a result known for analytic eigenfunctions of analytic systems.
关键词：KeywordsKoopman operatoreigenfunctionsgeneric propertiesisostablesperiodic orbits