FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2991844785> ?p ?o ?g. }

• W2991844785 endingPage "2145" @default.
• W2991844785 startingPage "2091" @default.
• W2991844785 abstract "We examine spectral operator-theoretic properties of linear and nonlinear dynamical systems with globally stable attractors. Using the Kato decomposition, we develop a spectral expansion for general linear autonomous dynamical systems with analytic observables and define the notion of generalized eigenfunctions of the associated Koopman operator. We interpret stable, unstable and center subspaces in terms of zero-level sets of generalized eigenfunctions. We then utilize conjugacy properties of Koopman eigenfunctions and the new notion of open eigenfunctions—defined on subsets of state space—to extend these results to nonlinear dynamical systems with an equilibrium. We provide a characterization of (global) center manifolds, center-stable, and center-unstable manifolds in terms of joint zero-level sets of families of Koopman operator eigenfunctions associated with the nonlinear system. After defining a new class of Hilbert spaces, that capture the on- and off-attractor properties of dissipative dynamics, and introducing the concept of modulated Fock spaces, we develop spectral expansions for a class of dynamical systems possessing globally stable limit cycles and limit tori, with observables that are square-integrable in on-attractor variables and analytic in off-attractor variables. We discuss definitions of stable, unstable, and global center manifolds in such nonlinear systems with (quasi)-periodic attractors in terms of zero-level sets of Koopman operator eigenfunctions. We define the notion of isostables for a general class of nonlinear systems. In contrast with the systems that have discrete Koopman operator spectrum, we provide a simple example of a measure-preserving system that is not chaotic but has continuous spectrum, and discuss experimental observations of spectrum on such systems. We also provide a brief characterization of the data types corresponding to the obtained theoretical results and define the coherent principal dimension for a class of datasets based on the lattice-type principal spectrum of the associated Koopman operator." @default.
• W2991844785 created "2019-12-13" @default.
• W2991844785 creator A5014334832 @default.
• W2991844785 date "2019-12-06" @default.
• W2991844785 modified "2023-10-16" @default.
• W2991844785 title "Spectrum of the Koopman Operator, Spectral Expansions in Functional Spaces, and State-Space Geometry" @default.
• W2991844785 cites W1551756560 @default.
• W2991844785 cites W1730162945 @default.
• W2991844785 cites W1975487887 @default.
• W2991844785 cites W1983964647 @default.
• W2991844785 cites W1990636640 @default.
• W2991844785 cites W1994953169 @default.
• W2991844785 cites W1995043136 @default.
• W2991844785 cites W1997054581 @default.
• W2991844785 cites W2013734438 @default.
• W2991844785 cites W2014356541 @default.
• W2991844785 cites W2016315007 @default.
• W2991844785 cites W2022911541 @default.
• W2991844785 cites W2067035505 @default.
• W2991844785 cites W2069159682 @default.
• W2991844785 cites W2069974243 @default.
• W2991844785 cites W2073505808 @default.
• W2991844785 cites W2079647387 @default.
• W2991844785 cites W2083115202 @default.
• W2991844785 cites W2094686470 @default.
• W2991844785 cites W2101222417 @default.
• W2991844785 cites W2114876173 @default.
• W2991844785 cites W2164954534 @default.
• W2991844785 cites W2172945660 @default.
• W2991844785 cites W2289369672 @default.
• W2991844785 cites W2289725842 @default.
• W2991844785 cites W2319450871 @default.
• W2991844785 cites W2482944896 @default.
• W2991844785 cites W2505615364 @default.
• W2991844785 cites W2567118861 @default.
• W2991844785 cites W2901625726 @default.
• W2991844785 cites W3038118776 @default.
• W2991844785 cites W3105713006 @default.
• W2991844785 cites W4239513491 @default.
• W2991844785 cites W4244334050 @default.
• W2991844785 cites W4294967943 @default.
• W2991844785 cites W4302585512 @default.
• W2991844785 doi "https://doi.org/10.1007/s00332-019-09598-5" @default.
• W2991844785 hasPublicationYear "2019" @default.
• W2991844785 type Work @default.
• W2991844785 sameAs 2991844785 @default.
• W2991844785 citedByCount "87" @default.
• W2991844785 countsByYear W29918447852018 @default.
• W2991844785 countsByYear W29918447852019 @default.
• W2991844785 countsByYear W29918447852020 @default.
• W2991844785 countsByYear W29918447852021 @default.
• W2991844785 countsByYear W29918447852022 @default.
• W2991844785 countsByYear W29918447852023 @default.
• W2991844785 crossrefType "journal-article" @default.
• W2991844785 hasAuthorship W2991844785A5014334832 @default.
• W2991844785 hasBestOaLocation W29918447852 @default.
• W2991844785 hasConcept C104317684 @default.
• W2991844785 hasConcept C121332964 @default.
• W2991844785 hasConcept C128803854 @default.
• W2991844785 hasConcept C134306372 @default.
• W2991844785 hasConcept C158448853 @default.
• W2991844785 hasConcept C158622935 @default.
• W2991844785 hasConcept C158693339 @default.
• W2991844785 hasConcept C164380108 @default.
• W2991844785 hasConcept C17020691 @default.
• W2991844785 hasConcept C185592680 @default.
• W2991844785 hasConcept C202444582 @default.
• W2991844785 hasConcept C32848918 @default.
• W2991844785 hasConcept C33923547 @default.
• W2991844785 hasConcept C33962884 @default.
• W2991844785 hasConcept C55493867 @default.
• W2991844785 hasConcept C62520636 @default.
• W2991844785 hasConcept C62799726 @default.
• W2991844785 hasConcept C79379906 @default.
• W2991844785 hasConcept C86339819 @default.
• W2991844785 hasConceptScore W2991844785C104317684 @default.
• W2991844785 hasConceptScore W2991844785C121332964 @default.
• W2991844785 hasConceptScore W2991844785C128803854 @default.
• W2991844785 hasConceptScore W2991844785C134306372 @default.
• W2991844785 hasConceptScore W2991844785C158448853 @default.
• W2991844785 hasConceptScore W2991844785C158622935 @default.
• W2991844785 hasConceptScore W2991844785C158693339 @default.
• W2991844785 hasConceptScore W2991844785C164380108 @default.
• W2991844785 hasConceptScore W2991844785C17020691 @default.
• W2991844785 hasConceptScore W2991844785C185592680 @default.
• W2991844785 hasConceptScore W2991844785C202444582 @default.
• W2991844785 hasConceptScore W2991844785C32848918 @default.
• W2991844785 hasConceptScore W2991844785C33923547 @default.
• W2991844785 hasConceptScore W2991844785C33962884 @default.
• W2991844785 hasConceptScore W2991844785C55493867 @default.
• W2991844785 hasConceptScore W2991844785C62520636 @default.
• W2991844785 hasConceptScore W2991844785C62799726 @default.
• W2991844785 hasConceptScore W2991844785C79379906 @default.
• W2991844785 hasConceptScore W2991844785C86339819 @default.
• W2991844785 hasFunder F4320332180 @default.
• W2991844785 hasFunder F4320338281 @default.
• W2991844785 hasIssue "5" @default.
• W2991844785 hasLocation W29918447851 @default.

• next