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First integrals of affine connections and Hamiltonian systems of hydrodynamic type

dc.creatorContatto, F
dc.creatorDunajski, Maciej Lukasz
dc.date.accessioned2016-07-25
dc.date.accessioned2018-11-24T23:20:38Z
dc.date.available2017-10-30T09:42:05Z
dc.date.available2018-11-24T23:20:38Z
dc.date.issued2016-12-23
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/267951
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/3621
dc.description.abstractWe find necessary and sufficient conditions for a local geodesic flow of an affine connection on a surface to admit a linear first integral. The conditions are expressed in terms of two scalar invariants of differential orders 3 and 4 in the connection. We use this result to find explicit obstructions to the existence of a Hamiltonian formulation of Dubrovin–Novikov type for a given one-dimensional system of hydrodynamic type. We give several examples including Zoll connections, and Hamiltonian systems arising from twodimensional Frobenius manifolds.
dc.languageen
dc.publisherOxford University Press
dc.publisherJournal of Integrable Systems
dc.rightshttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rightshttp://creativecommons.org/licenses/by-nc/4.0/
dc.rightshttp://creativecommons.org/licenses/by-nc/4.0/
dc.rightshttp://creativecommons.org/licenses/by-nc/4.0/
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International
dc.rightsAttribution-NonCommercial 4.0 International
dc.rightsAttribution-NonCommercial 4.0 International
dc.rightsAttribution-NonCommercial 4.0 International
dc.subjectmath.DG
dc.subjectmath.DG
dc.subjecthep-th
dc.subjectnlin.SI
dc.subjectaffine connections
dc.subjectHamiltonian systems
dc.subjecthydrodynamic type
dc.titleFirst integrals of affine connections and Hamiltonian systems of hydrodynamic type
dc.typeArticle


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