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Density Evolution Under Delayed Dyna...
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Losson, Jérôme.
Density Evolution Under Delayed Dynamics = An Open Problem /
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Density Evolution Under Delayed Dynamics/ by Jérôme Losson, Michael C. Mackey, Richard Taylor, Marta Tyran-Kamińska.
其他題名:
An Open Problem /
作者:
Losson, Jérôme.
其他作者:
Mackey, Michael C.
面頁冊數:
IX, 138 p. 37 illus., 9 illus. in color.online resource. :
Contained By:
Springer Nature eBook
標題:
Mathematical analysis. -
電子資源:
https://doi.org/10.1007/978-1-0716-1072-5
ISBN:
9781071610725
Density Evolution Under Delayed Dynamics = An Open Problem /
Losson, Jérôme.
Density Evolution Under Delayed Dynamics
An Open Problem /[electronic resource] :by Jérôme Losson, Michael C. Mackey, Richard Taylor, Marta Tyran-Kamińska. - 1st ed. 2020. - IX, 138 p. 37 illus., 9 illus. in color.online resource. - Fields Institute Monographs,381069-5273 ;. - Fields Institute Monographs,34.
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.
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. .
ISBN: 9781071610725
Standard No.: 10.1007/978-1-0716-1072-5doiSubjects--Topical Terms:
527926
Mathematical analysis.
LC Class. No.: QA299.6-433
Dewey Class. No.: 515
Density Evolution Under Delayed Dynamics = An Open Problem /
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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.
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