03789nam a22005175i 4500 978-981-97-5520-2 DE-He213 20251030114645.0 cr nn 008mamaa 241227s2024 si | s |||| 0|eng d 9789819755202 978-981-97-5520-2 10.1007/978-981-97-5520-2 doi QA843-871 GPFC bicssc MAT034000 bisacsh GPFC thema Doan, Thai Son. author. aut http://id.loc.gov/vocabulary/relators/aut 89721 Spectral Theory of Nonautonomous Dynamical Systems and Applications [electronic resource] / by Thai Son Doan. 1st ed. 2024. Singapore : Springer Nature Singapore : Imprint: Springer, 2024. XVII, 188 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 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. Dynamical systems. Differential equations. Stochastic processes. 76770 Dynamical Systems. Differential Equations. Stochastic Processes. 76770 SpringerLink (Online service) Springer Nature eBook Printed edition: 9789819755196 Printed edition: 9789819755219 Printed edition: 9789819755226 https://doi.org/10.1007/978-981-97-5520-2 ZDB-2-SMA ZDB-2-SXMS 66114 66114