Time-Varying Vector Fields and Their Flows

• Κύριοι συγγραφείς: Jafarpour, Saber (Συγγραφέας), Lewis, Andrew D. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Σειρά: SpringerBriefs in Mathematics,
• Θέματα: Mathematics.; Topological groups.; Lie groups.; Dynamics.; Ergodic theory.; System theory.; Systems Theory, Control.; Dynamical Systems and Ergodic Theory.; Topological Groups, Lie Groups.

 This short book provides a comprehensive and unified treatment of time-varying vector fields under a variety of regularity hypotheses, namely finitely differentiable, Lipschitz, smooth, holomorphic, and real analytic. The presentation of this material in the real analytic setting is new, as is the manner in which the various hypotheses are unified using functional analysis. Indeed, a major contribution of the book is the coherent development of locally convex topologies for the space of real analytic sections of a vector bundle, and the development of this in a manner that relates easily to classically known topologies in, for example, the finitely differentiable and smooth cases. The tools used in this development will be of use to researchers in the area of geometric functional analysis. 

 Introduction -- Fibre Metrics for Jet Bundles -- Finitely Differentiable, Lipschitz, and Smooth Topologies -- The COhol-topology for the Space of Holomorphic Vector Fields -- The Cw-topology for the Space of Real Analytic Vector Fields -- Time-Varying Vector Fields -- References.