國立虎尾科技大學 |

Density Evolution Under Delayed Dynamics = An Open Problem /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Density Evolution Under Delayed Dynamics/ by Jérôme Losson, Michael C. Mackey, Richard Taylor, Marta Tyran-Kamińska.
Reminder of title:	An Open Problem /
Author:	Losson, Jérôme.
other author:	Mackey, Michael C.
Description:	IX, 138 p. 37 illus., 9 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mathematical analysis. -
Online resource:	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 DynamicsAn 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 /
LDR:02881nam a22004095i 4500 001 1025594
003 DE-He213
005 20201023114808.0
007 cr nn 008mamaa
008 210318s2020 xxu| s |||| 0|eng d
020 $a 9781071610725 $9 978-1-0716-1072-5
024 7 $a 10.1007/978-1-0716-1072-5 $2 doi
035 $a 978-1-0716-1072-5
050 4 $a QA299.6-433
072 7 $a PBK $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBK $2 thema
082 0 4 $a 515 $2 23
100 1 $a Losson, Jérôme. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1321879
245 1 0 $a Density Evolution Under Delayed Dynamics $h [electronic resource] : $b An Open Problem / $c by Jérôme Losson, Michael C. Mackey, Richard Taylor, Marta Tyran-Kamińska.
250 $a 1st ed. 2020.
264 1 $a New York, NY : $b Springer US : $b Imprint: Springer, $c 2020.
300 $a IX, 138 p. 37 illus., 9 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Fields Institute Monographs, $x 1069-5273 ; $v 38
505 0 $a 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.
520 $a 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. .
650 0 $a Mathematical analysis. $3 527926
650 0 $a Analysis (Mathematics). $3 1253570
650 0 $a Measure theory. $3 527848
650 0 $a Dynamics. $3 592238
650 0 $a Ergodic theory. $3 672355
650 0 $a Vibration. $3 595749
650 0 $a Dynamical systems. $3 1249739
650 0 $a Probabilities. $3 527847
650 1 4 $a Analysis. $3 669490
650 2 4 $a Measure and Integration. $3 672015
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 671353
650 2 4 $a Vibration, Dynamical Systems, Control. $3 670825
650 2 4 $a Probability Theory and Stochastic Processes. $3 593945
700 1 $a Mackey, Michael C. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1115821
700 1 $a Taylor, Richard. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1321880
700 1 $a Tyran-Kamińska, Marta. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1267842
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9781071610718
776 0 8 $i Printed edition: $z 9781071610732
776 0 8 $i Printed edition: $z 9781071610749
830 0 $a Fields Institute Monographs, $x 1069-5273 ; $v 34 $3 1265475
856 4 0 $u https://doi.org/10.1007/978-1-0716-1072-5
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)