Overview
- Describes an open and difficult mathematical problem, offering a new research field for young investigators
- Gives a brief but unified contrasting description of examination of dynamics from a trajectory or an ensemble point of view
- Highlights all of the problems attendant to the development of an appropriate measure to examine ergodic behavior in infinite-dimensional dynamical systems
- Presents possible applications of functional calculus to infinite dimensional dynamical systems
- Offers a motivated area of research combining different fields of mathematics
Part of the book series: Fields Institute Monographs (FIM, volume 38)
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About this book
This monograph has arisen out of a number of attempts spanning almost five decades to understand how one might examine the evolution of densities in systems whose dynamics are described by differential delay equations. Though the authors have no definitive solution to the problem, they offer this contribution in an attempt to define the problem as they see it, and to sketch out several obvious attempts that have been suggested to solve the problem and which seem to have failed. They hope that by being available to the general mathematical community, they will inspire others to consider–and hopefully solve–the problem. Serious attempts have been made by all of the authors over the years and they have made reference to these where appropriate.
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Table of contents (9 chapters)
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Front Matter
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Introduction and Background to Density Evolution Problems
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Front Matter
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Illustrating the Problem and Making It Precise for Differential Delay Equations
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Front Matter
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Possible Analytical Approaches
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Front Matter
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Back Matter
Reviews
“The book is devoted to the problem of evolution of densities in dynamical systems described by delay differential equations. … The book is interesting and introduces the reader to the problem of the evolution of the densities. Indeed, formulating (if possible) such an evolution one is able to guess the asymptotic behavior of the solutions with known density of their initial values. The examples in the book are carefully selected in order to illustrate the main theoretical results.” (George Karakostas, zbMATH 1462.37001, 2021)
Authors and Affiliations
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Bibliographic Information
Book Title: Density Evolution Under Delayed Dynamics
Book Subtitle: An Open Problem
Authors: Jérôme Losson, Michael C. Mackey, Richard Taylor, Marta Tyran-Kamińska
Series Title: Fields Institute Monographs
DOI: https://doi.org/10.1007/978-1-0716-1072-5
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2020
Hardcover ISBN: 978-1-0716-1071-8Published: 24 October 2020
Softcover ISBN: 978-1-0716-1074-9Published: 24 October 2021
eBook ISBN: 978-1-0716-1072-5Published: 23 October 2020
Series ISSN: 1069-5273
Series E-ISSN: 2194-3079
Edition Number: 1
Number of Pages: IX, 138
Number of Illustrations: 28 b/w illustrations, 9 illustrations in colour
Topics: Analysis, Measure and Integration, Dynamical Systems and Ergodic Theory, Vibration, Dynamical Systems, Control, Probability Theory and Stochastic Processes