Infinite-dimensional second order ordinary differential equations via

Autor:	George Galanis, Mansour Aghasi, A. Suri, Christopher T. J. Dodson
Rok vydání:	2007
Předmět:	Tangent bundle Vector-valued differential form Parallel transport Applied Mathematics Mathematical analysis Vector bundle Affine connection symbols.namesake Normal bundle Global analysis symbols Frobenius theorem (differential topology) Analysis Mathematics
Zdroj:	Nonlinear Analysis: Theory, Methods & Applications. 67:2829-2838
ISSN:	0362-546X
DOI:	10.1016/j.na.2006.09.043
Popis:	The vector bundle structure obtained on the second order (acceleration) tangent bundle T 2 M of a smooth manifold M by means of a linear connection on the base provides an alternative way for the study of second order ordinary differential equations on manifolds of finite and infinite dimension. Second order vector fields and their integral curves could provide a new way of representing and solving a wide class of evolutionary equations for states on Frechet manifolds of sections that arise naturally as inequivalent configurations of a physical field. The technique is illustrated by examples in the framework of Banach and Frechet spaces, and on Lie groups, in particular discussing the case of autoparallel curves, which include geodesics if the connection is induced by a Riemannian structure.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::aec7191629b1ab98c72d217e2d849680 https://doi.org/10.1016/j.na.2006.09.043 Zobrazit plný text záznamu Full Text from ScienceDirect