LEADER 02999nam 2200517 450 001 9910484050403321 005 20210331232346.0 010 $a1-0716-1072-4 024 7 $a10.1007/978-1-0716-1072-5 035 $a(CKB)4100000011515531 035 $a(DE-He213)978-1-0716-1072-5 035 $a(MiAaPQ)EBC6381215 035 $a(PPN)258061669 035 $a(EXLCZ)994100000011515531 100 $a20210331d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDensity evolution under delayed dynamics $ean open problem /$fJe?ro?me Losson, 3 others 205 $a1st ed. 2020. 210 1$aNew York, New York :$cSpringer,$d[2020] 210 4$dİ2020 215 $a1 online resource (IX, 138 p. 37 illus., 9 illus. in color.) 225 1 $aFields Institute Monographs,$x1069-5273 ;$v38 311 $a1-0716-1071-6 320 $aIncludes bibliographical references and index. 327 $aPart 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. 330 $aThis monograph has arisen out of a number of attempts spanning almost five decades to understand how one might examine the evolution of densities in systems whose dynamics are described by differential delay equations. Though the authors have no definitive solution to the problem, they offer this contribution in an attempt to define the problem as they see it, and to sketch out several obvious attempts that have been suggested to solve the problem and which seem to have failed. They hope that by being available to the general mathematical community, they will inspire others to consider?and hopefully solve?the problem. Serious attempts have been made by all of the authors over the years and they have made reference to these where appropriate. . 410 0$aFields Institute Monographs,$x1069-5273 ;$v38 606 $aDelay differential equations 606 $aMathematical analysis 606 $aMeasure theory 615 0$aDelay differential equations. 615 0$aMathematical analysis. 615 0$aMeasure theory. 676 $a515 700 $aLosson$b Je?ro?me$0900688 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484050403321 996 $aDensity evolution under delayed dynamics$92013027 997 $aUNINA