Time-Varying Vector Fields and Their Flows

Nonfiction, Science & Nature, Science, Other Sciences, System Theory, Mathematics, Mathematical Analysis, Reference & Language, Reference
Cover of the book Time-Varying Vector Fields and Their Flows by Saber Jafarpour, Andrew D. Lewis, Springer International Publishing
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Author: Saber Jafarpour, Andrew D. Lewis ISBN: 9783319101392
Publisher: Springer International Publishing Publication: October 10, 2014
Imprint: Springer Language: English
Author: Saber Jafarpour, Andrew D. Lewis
ISBN: 9783319101392
Publisher: Springer International Publishing
Publication: October 10, 2014
Imprint: Springer
Language: English

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.

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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.

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