Density evolution under delayed dynamics : an open problem / Jérôme Losson, Michael C. Mackey, Richard Taylor, Marta Tyran-Kamińska.

Format:

Book

Author/Creator:

Losson, Jérôme, author.

Mackey, Michael C., 1942- author.

Taylor, S. Richard, 1975- author.

Tyran-Kamińska, Marta, author.

Series:

Fields Institute monographs ; 38.

Fields Institute monographs, 1069-5273 ; volume 38

Language:

English

Subjects (All):

Delay differential equations.

Mathematical analysis.

Measure theory.

Dynamics.

Ergodic theory.

Vibration.

Probabilities.

Physical Description:

ix, 138 pages : illustrations (some color) ; 25 cm.

Place of Publication:

New York : Springer ; [ Toronto, Canada] : Fields Institute for Research in the Mathematical Sciences, [2020]

Summary:

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. .

Contents:

Part I. Introduction and Background to Density Evolution Problems

1. Introduction and Motivation

2. Density Evolution in Systems with Finite Dimensional Dynamics

Part II. Illustrating the Problem and Making it Precise for Differential Delay Equations

3. Dynamics in Ensembles of Differential Delay Equations

4. The Problem

III. Possible Analytical Approaches

5. The Hopf Functional Approach

6. The Method of Steps

Part IV. Possible Approximating Solutions

7. Turning a Differential Delay Equation into a High-Dimensional Map

8. Approximate "Liouville-like" Equation

9. Summary and Conclusions

References

Index.

Notes:

Includes bibliographical references and index.

British Library not licensed to copy 0.

ISBN:

9781071610718

1071610716

OCLC:

1164500123

Publisher Number:

10.1007/978-1-0716-1072-5