LEADER 03702nam 22005775 450 001 9910919812003321 005 20251113202410.0 010 $a9789819755202 010 $a9819755204 024 7 $a10.1007/978-981-97-5520-2 035 $a(MiAaPQ)EBC31862484 035 $a(Au-PeEL)EBL31862484 035 $a(CKB)37093814900041 035 $a(DE-He213)978-981-97-5520-2 035 $a(EXLCZ)9937093814900041 100 $a20241227d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSpectral Theory of Nonautonomous Dynamical Systems and Applications /$fby Thai Son Doan 205 $a1st ed. 2024. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2024. 215 $a1 online resource (200 pages) 311 08$a9789819755196 311 08$a9819755190 320 $aIncludes bibliographical references and index. 327 $achapter 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. 330 $aThe 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. 606 $aDynamics 606 $aDifferential equations 606 $aStochastic processes 606 $aDynamical Systems 606 $aDifferential Equations 606 $aStochastic Processes 615 0$aDynamics. 615 0$aDifferential equations. 615 0$aStochastic processes. 615 14$aDynamical Systems. 615 24$aDifferential Equations. 615 24$aStochastic Processes. 676 $a515.352 700 $aDoan$b Thai Son$01781568 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910919812003321 996 $aSpectral Theory of Nonautonomous Dynamical Systems and Applications$94306419 997 $aUNINA