國立高雄大學圖資館 |

Language: English

Back

Spectral theory of nonautonomous dynamical systems and applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	Spectral theory of nonautonomous dynamical systems and applicationsby Thai Son Doan.
Author:	Doan, Thai Son.
Published:	Singapore :Springer Nature Singapore :2024.
Description:	xvii, 188 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Differentiable dynamical systems.
Online resource:	https://doi.org/10.1007/978-981-97-5520-2
ISBN:	9789819755202$q(electronic bk.)

Spectral theory of nonautonomous dynamical systems and applications
Doan, Thai Son.

Spectral theory of nonautonomous dynamical systems and applications[electronic resource] /by Thai Son Doan. - Singapore :Springer Nature Singapore :2024. - xvii, 188 p. :ill., digital ;24 cm.

chapter 1 spectral theory of nonautonomous differential equations -- chapter 2 linearization for nonautonomous differential equations -- chapter 3 spectral theory for random dynamical systems -- chapter 4 genericity of lyapunov spectrum of random dynamical systems -- chapter 5 pitchfork and hopf bifurcation under additive noise.

The main challenge in the study of nonautonomous phenomena is to understand the very complicated dynamical behaviour both as a scientific and mathematical problem. The theory of nonautonomous dynamical systems has experienced a renewed and steadily growing interest in the last twenty years, stimulated also by synergetic effects of disciplines which have developed relatively independent for some time such as topological skew product, random dynamical systems, finite-time dynamics and control systems. The book provides new insights in many aspects of the qualitative theory of nonautonomous dynamical systems including the spectral theory, the linearization theory, the bifurcation theory. The book first introduces several important spectral theorem for nonautonomous differential equations including the Lyapunov spectrum, Sacker-Sell spectrum and finite-time spectrum. The author also establishes the smooth linearization and partial linearization for nonautonomous differential equations in application part. Then the second part recalls the multiplicative ergodic theorem for random dynamical systems and discusses several explicit formulas in computing the Lyapunov spectrum for random dynamical systems generated by linear stochastic differential equations and random difference equations with random delay. In the end, the Pitchfork bifurcation and Hopf bifurcation with additive noise are investigated in terms of change of the sign of Lyapunov exponents and loss of topological equivalence. This book might be appealing to researchers and graduate students in the field of dynamical systems, stochastic differential equations, ergodic theory.

ISBN: 9789819755202$q(electronic bk.)

Standard No.: 10.1007/978-981-97-5520-2doiSubjects--Topical Terms:

183764
Differentiable dynamical systems.

LC Class. No.: QA614.8

Dewey Class. No.: 515.352

Spectral theory of nonautonomous dynamical systems and applications
LDR:02980nmm a2200325 a 4500 001 673506
003 DE-He213
005 20241227115307.0
006 m d
007 cr nn 008maaau
008 250422s2024 si s 0 eng d
020 $a 9789819755202$q(electronic bk.)
020 $a 9789819755196$q(paper)
024 7 $a 10.1007/978-981-97-5520-2 $2 doi
035 $a 978-981-97-5520-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA614.8
072 7 $a GPFC $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a GPFC $2 thema
082 0 4 $a 515.352 $2 23
090 $a QA614.8 $b .D631 2024
100 1 $a Doan, Thai Son. $3 987039
245 1 0 $a Spectral theory of nonautonomous dynamical systems and applications $h [electronic resource] / $c by Thai Son Doan.
260 $a Singapore : $b Springer Nature Singapore : $b Imprint: Springer, $c 2024.
300 $a xvii, 188 p. : $b ill., digital ; $c 24 cm.
505 0 $a chapter 1 spectral theory of nonautonomous differential equations -- chapter 2 linearization for nonautonomous differential equations -- chapter 3 spectral theory for random dynamical systems -- chapter 4 genericity of lyapunov spectrum of random dynamical systems -- chapter 5 pitchfork and hopf bifurcation under additive noise.
520 $a The main challenge in the study of nonautonomous phenomena is to understand the very complicated dynamical behaviour both as a scientific and mathematical problem. The theory of nonautonomous dynamical systems has experienced a renewed and steadily growing interest in the last twenty years, stimulated also by synergetic effects of disciplines which have developed relatively independent for some time such as topological skew product, random dynamical systems, finite-time dynamics and control systems. The book provides new insights in many aspects of the qualitative theory of nonautonomous dynamical systems including the spectral theory, the linearization theory, the bifurcation theory. The book first introduces several important spectral theorem for nonautonomous differential equations including the Lyapunov spectrum, Sacker-Sell spectrum and finite-time spectrum. The author also establishes the smooth linearization and partial linearization for nonautonomous differential equations in application part. Then the second part recalls the multiplicative ergodic theorem for random dynamical systems and discusses several explicit formulas in computing the Lyapunov spectrum for random dynamical systems generated by linear stochastic differential equations and random difference equations with random delay. In the end, the Pitchfork bifurcation and Hopf bifurcation with additive noise are investigated in terms of change of the sign of Lyapunov exponents and loss of topological equivalence. This book might be appealing to researchers and graduate students in the field of dynamical systems, stochastic differential equations, ergodic theory.
650 0 $a Differentiable dynamical systems. $3 183764
650 0 $a Differential equations. $3 183925
650 0 $a Spectral theory (Mathematics) $3 182365
650 1 4 $a Dynamical Systems. $3 913342
650 2 4 $a Differential Equations. $3 285983
650 2 4 $a Stochastic Processes. $3 743764
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-981-97-5520-2
950 $a Mathematics and Statistics (SpringerNature-11649)