03573nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001700186072002300203072001600226100008400242245011600326250001800442264007200460300003500532336002600567337002600593338003600619347002400655505033500679520166101014650002302675650002802698650003302726650002302759650002802782650003302810710003402843773002602877776003602903776003602939776003602975856004603011912001403057912001503071999001703086978-981-97-5520-2DE-He21320251030114645.0cr nn 008mamaa241227s2024    si |    s    |||| 0|eng d  a97898197552029978-981-97-5520-27 a10.1007/978-981-97-5520-22doi 4aQA843-871 7aGPFC2bicssc 7aMAT0340002bisacsh 7aGPFC2thema1 aDoan, Thai Son.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98972110aSpectral Theory of Nonautonomous Dynamical Systems and Applicationsh[electronic resource] /cby Thai Son Doan.  a1st ed. 2024. 1aSingapore :bSpringer Nature Singapore :bImprint: Springer,c2024.  aXVII, 188 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 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.  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. 0aDynamical systems. 0aDifferential equations. 0aStochastic processes.97677014aDynamical Systems.24aDifferential Equations.24aStochastic Processes.9767702 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978981975519608iPrinted edition:z978981975521908iPrinted edition:z978981975522640uhttps://doi.org/10.1007/978-981-97-5520-2  aZDB-2-SMA  aZDB-2-SXMS  c66114d66114