Time-Varying Vector Fields and Their Flows

1. Front Matter

   Pages i-viii

   PDF

2. Introduction

   • Saber Jafarpour, Andrew D. Lewis

   Pages 1-13

3. Fibre Metrics for Jet Bundles

   • Saber Jafarpour, Andrew D. Lewis

   Pages 15-43

4. The Compact-Open Topologies for the Spaces of Finitely Differentiable, Lipschitz, and Smooth Vector Fields

   • Saber Jafarpour, Andrew D. Lewis

   Pages 45-64

5. The COhol-Topology for the Space of Holomorphic Vector Fields

   • Saber Jafarpour, Andrew D. Lewis

   Pages 65-71

6. The C^ω-Topology for the Space of Real Analytic Vector Fields

   • Saber Jafarpour, Andrew D. Lewis

   Pages 73-92

7. Time-Varying Vector Fields

   • Saber Jafarpour, Andrew D. Lewis

   Pages 93-119

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.

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

“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)

• Department of Mathematics and Statistics, Queen's University, Kingston, Canada

  Saber Jafarpour, Andrew D. Lewis

Saber Jafarpour is a PhD candidate in Queen's University's Department of Mathematics and Statistics, Canada.

Andrew D. Lewis is a Professor of Mathematics at Queen's University.  His research interests include control of mechanical systems, geometric mechanics, and nonlinear control.

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