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• W1970455529 abstract "A centerpiece of dynamical systems is comparison by an equivalence relationship called topological conjugacy. We present details of how a method to produce conjugacy functions based on a functional fixed point iteration scheme can be generalized to compare dynamical systems that are not conjugate. When applied to nonconjugate dynamical systems, we show that the fixed-point iteration scheme still has a limit point, which is a function we now call a “commuter”—a nonhomeomorphic change of coordinates translating between dissimilar systems. This translation is natural to the concepts of dynamical systems in that it matches the systems within the language of their orbit structures, meaning that orbits must be matched to orbits by some commuter function. We introduce methods to compare nonequivalent systems by quantifying how much the commuter function fails to be a homeomorphism, an approach that gives more respect to the dynamics than the traditional comparisons based on normed linear spaces, such as L2. Our discussion addresses a fundamental issue—how does one make principled statements of the degree to which a “toy model” might be representative of a more complicated system?" @default.
• W1970455529 created "2016-06-24" @default.
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• W1970455529 date "2008-03-01" @default.
• W1970455529 modified "2023-09-25" @default.
• W1970455529 title "A concept of homeomorphic defect for defining mostly conjugate dynamical systems" @default.
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• W1970455529 doi "https://doi.org/10.1063/1.2837397" @default.
• W1970455529 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/18377069" @default.
• W1970455529 hasPublicationYear "2008" @default.
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