Time-Varying Vector Fields and Their Flows
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.
The conditions for joint dependence on state and time are given for a real analytic time-varying vector field to have a flow depending on initial condition in a real analytic mannerPresents a united framework for performing analysis on vector bundles in a variety of regularity classesAn explicit description is given for the topology of the space of real analytic sections of a vector bundleOffers a unified treatment of time-varying vector fields for all common regularity classes