Type of Publication:  Journal article 
Publication status:  Published 
Author:  Pavlovic, Dusko; Fauser, Bertfried 
Year of publication:  2017 
Published in:  Mathematical Structures in Computer Science ; 27 (2017), 7.  pp. 11951235.  ISSN 09601295.  eISSN 14698072 
ArXivID:  arXiv:1402.4414v2 
DOI (citable link):  https://dx.doi.org/10.1017/S0960129515000511 
Summary: 
Processes are often viewed as coalgebras, with the structure maps specifying the state transitions. In the simplest case, the state spaces are discrete, and the structure map simply takes each state to the next states. But the coalgebraic view is also quite effective for studying processes over structured state spaces, e.g. measurable, or continuous. In the present paper, we consider coalgebras over manifolds. This means that the captured processes evolve over state spaces that are not just continuous, but also locally homeomorphic to normed vector spaces, and thus carry a differential structure. Both dynamical systems and differential forms arise as coalgebras over such state spaces, for two different endofunctors over manifolds. A duality induced by these two endofunctors provides a formal underpinning for the informal geometric intuitions linking differential forms and dynamical systems in the various practical applications, e.g. in physics. This joint functorial reconstruction of tangent bundles and cotangent bundles uncovers the universal properties and a highlevel view of these fundamental structures, which are implemented rather intricately in their standard form. The succinct coalgebraic presentation provides unexpected insights even about the situations as familiar as Newton's laws.

Subject (DDC):  530 Physics 
Files  Size  Format  View 

There are no files associated with this item. 
PAVLOVIC, Dusko, Bertfried FAUSER, 2017. Smooth coalgebra : testing vector analysis. In: Mathematical Structures in Computer Science. 27(7), pp. 11951235. ISSN 09601295. eISSN 14698072. Available under: doi: 10.1017/S0960129515000511
@article{Pavlovic2017Smoot41158, title={Smooth coalgebra : testing vector analysis}, year={2017}, doi={10.1017/S0960129515000511}, number={7}, volume={27}, issn={09601295}, journal={Mathematical Structures in Computer Science}, pages={11951235}, author={Pavlovic, Dusko and Fauser, Bertfried} }
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22rdfsyntaxns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digitalrepositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.unikonstanz.de/rdf/resource/123456789/41158"> <dcterms:abstract xml:lang="eng">Processes are often viewed as coalgebras, with the structure maps specifying the state transitions. In the simplest case, the state spaces are discrete, and the structure map simply takes each state to the next states. But the coalgebraic view is also quite effective for studying processes over structured state spaces, e.g. measurable, or continuous. In the present paper, we consider coalgebras over manifolds. This means that the captured processes evolve over state spaces that are not just continuous, but also locally homeomorphic to normed vector spaces, and thus carry a differential structure. Both dynamical systems and differential forms arise as coalgebras over such state spaces, for two different endofunctors over manifolds. A duality induced by these two endofunctors provides a formal underpinning for the informal geometric intuitions linking differential forms and dynamical systems in the various practical applications, e.g. in physics. This joint functorial reconstruction of tangent bundles and cotangent bundles uncovers the universal properties and a highlevel view of these fundamental structures, which are implemented rather intricately in their standard form. The succinct coalgebraic presentation provides unexpected insights even about the situations as familiar as Newton's laws.</dcterms:abstract> <dcterms:isPartOf rdf:resource="https://kops.unikonstanz.de/rdf/resource/123456789/41"/> <dspace:isPartOfCollection rdf:resource="https://kops.unikonstanz.de/rdf/resource/123456789/41"/> <dc:creator>Fauser, Bertfried</dc:creator> <dc:creator>Pavlovic, Dusko</dc:creator> <dcterms:issued>2017</dcterms:issued> <dc:language>eng</dc:language> <dc:contributor>Pavlovic, Dusko</dc:contributor> <bibo:uri rdf:resource="https://kops.unikonstanz.de/handle/123456789/41158"/> <dc:contributor>Fauser, Bertfried</dc:contributor> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">20180125T10:30:31Z</dcterms:available> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:title>Smooth coalgebra : testing vector analysis</dcterms:title> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">20180125T10:30:31Z</dc:date> </rdf:Description> </rdf:RDF>