Ontology type: schema:ScholarlyArticle
2019-04-02
AUTHORSSuddhasattwa Das, Dimitrios Giannakis
ABSTRACTThe Koopman operator induced by a dynamical system is inherently linear and provides an alternate method of studying many properties of the system, including attractor reconstruction and forecasting. Koopman eigenfunctions represent the non-mixing component of the dynamics. They factor the dynamics, which can be chaotic, into quasiperiodic rotations on tori. Here, we describe a method through which these eigenfunctions can be obtained from a kernel integral operator, which also annihilates the continuous spectrum. We show that incorporating a large number of delay coordinates in constructing the kernel of that operator results, in the limit of infinitely many delays, in the creation of a map into the point spectrum subspace of the Koopman operator. This enables efficient approximation of Koopman eigenfunctions in systems with pure point or mixed spectra. We illustrate our results with applications to product dynamical systems with mixed spectra. More... »
PAGES1-39
http://scigraph.springernature.com/pub.10.1007/s10955-019-02272-w
DOIhttp://dx.doi.org/10.1007/s10955-019-02272-w
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"description": "The Koopman operator induced by a dynamical system is inherently linear and provides an alternate method of studying many properties of the system, including attractor reconstruction and forecasting. Koopman eigenfunctions represent the non-mixing component of the dynamics. They factor the dynamics, which can be chaotic, into quasiperiodic rotations on tori. Here, we describe a method through which these eigenfunctions can be obtained from a kernel integral operator, which also annihilates the continuous spectrum. We show that incorporating a large number of delay coordinates in constructing the kernel of that operator results, in the limit of infinitely many delays, in the creation of a map into the point spectrum subspace of the Koopman operator. This enables efficient approximation of Koopman eigenfunctions in systems with pure point or mixed spectra. We illustrate our results with applications to product dynamical systems with mixed spectra.",
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"url": "https://link.springer.com/10.1007%2Fs10955-019-02272-w"
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]Download the RDF metadata as: json-ld nt turtle xml License info
JSON-LD is a popular format for linked data which is fully compatible with JSON.
curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s10955-019-02272-w'
N-Triples is a line-based linked data format ideal for batch operations.
curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s10955-019-02272-w'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10955-019-02272-w'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10955-019-02272-w'
This table displays all metadata directly associated to this object as RDF triples.
245 TRIPLES
21 PREDICATES
81 URIs
16 LITERALS
5 BLANK NODES