Time-Varying Vector Fields and Their Flows

Beschreibung

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 manner Presents a united framework for performing analysis on vector bundles in a variety of regularity classes An explicit description is given for the topology of the space of real analytic sections of a vector bundle Offers a unified treatment of time-varying vector fields for all common regularity classes

Autor*in

Saber Jafarpour

Themen in »Time-Varying Vector Fields and Their Flows«

Fiber Metrics Real Analyticity Time-varying vector fields, real analytic geometry topologies for spaces of sections of vector bundles

Stimmen zu »Time-Varying Vector Fields and Their Flows«

“It presents a unified framework for the study of time-varying vector fields with measurable time dependence and different degree of regularity in the state variable. The monograph is well designed for those wanting to be introduced to the rudiments of the theory.” (Wojciech Kryszewski, Mathematical Reviews, December, 2015)

“The monograph is devoted to time-varying vector fields with measurable time dependence and with varying degrees of regularity in state … . The authors treat all regularity classes, includintg the real analytic one, which has been not studied in detail up till now. … the book is well written. That is why I recommend it to specialists in mathematics, physics and also to specialists in control theory.” (Miroslaw Doupovec, zbMATH 1321.58001, 2015)

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