Density Evolution Under Delayed Dynamics (eBook) von Jérôme Losson
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ISBN-13:
9781071610725
Veröffentl:
2020
Einband:
eBook
Seiten:
138
Autor:
Jérôme Losson
Serie:
38, Fields Institute Monographs
eBook Format:
PDF
eBook-Typ:
Reflowable eBook
Kopierschutz:
Digital Watermark [Social-DRM]
Sprache:
Englisch
Inhaltsverzeichnis
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.
Beschreibung
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 considerand hopefully solvethe problem. Serious attempts have been made by all of the authors over the years and they have made reference to these where appropriate.
Schlagwörter zu:
Density Evolution Under Delayed Dynamics von Jérôme Losson - mit der ISBN: 9781071610725
Hopf characteristic functionals; Markov processes; applications of functional calculus; ergodic theory; infinite-dimensional spaces; ordinary differential equations; B; Probability Theory; Measure and Integration; Dynamical Systems; Differential Equations; Mathematics and Statistics, Online-Buchhandlung
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