LEADER 03766nam 2200493 450 001 9910686474803321 005 20230616180257.0 010 $a9783031251542$b(electronic bk.) 010 $z9783031251535 024 7 $a10.1007/978-3-031-25154-2 035 $a(MiAaPQ)EBC7235423 035 $a(Au-PeEL)EBL7235423 035 $a(DE-He213)978-3-031-25154-2 035 $a(OCoLC)1375994966 035 $a(PPN)269657525 035 $a(EXLCZ)9926428011400041 100 $a20230616d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDynamical system and chaos $ean introduction with applications /$fRui Dila?o 205 $a1st ed. 2023. 210 1$aCham, Switzerland :$cSpringer,$d[2023] 210 4$d©2023 215 $a1 online resource (328 pages) 225 1 $aUNITEXT for Physics,$x2198-7890 311 08$aPrint version: Dilão, Rui Dynamical System and Chaos Cham : Springer International Publishing AG,c2023 9783031251535 327 $aDifferential Equations as Dynamical Systems -- Stability of fixed points -- Difference equations as dynamical systems -- Classification of fixed points -- Hamiltonian systems -- Numerical Methods.-Strange Attractors and Maps of an Interval -- Stable, Unstable and Centre manifolds.-Dynamics in the Centre Manifold -- Lyapunov Exponents and Oseledets Theorem -- Chaos -- Limit and Recurrent Sets.-Poincare Maps -- The Poincare-Bendixon Theorem -- Bifurcations of Differential Equations.-Singular Pertubations and Ducks.-Strange Attractors in Delay Equations -- Complexity of Strange Attractors.-Intermittency -- Cellular Automata -- Maps of the Complex Plane -- Stochastic Iteration of Function Systems -- Linear Maps on the Torus and Symbolic Dynamics -- Parametric Resonance -- Robot Motion -- Synchronisation of Pendula -- Synchronisation of Clocks -- Chaos in Stormer Problem.-Introduction to Celestial mechanics -- Introduction to non-Liner control Theory -- Appendices. 330 $aThis textbook introduces the language and the techniques of the theory of dynamical systems of finite dimension for an audience of physicists, engineers, and mathematicians at the beginning of graduation. Author addresses geometric, measure, and computational aspects of the theory of dynamical systems. Some freedom is used in the more formal aspects, using only proofs when there is an algorithmic advantage or because a result is simple and powerful. The first part is an introductory course on dynamical systems theory. It can be taught at the master's level during one semester, not requiring specialized mathematical training. In the second part, the author describes some applications of the theory of dynamical systems. Topics often appear in modern dynamical systems and complexity theories, such as singular perturbation theory, delayed equations, cellular automata, fractal sets, maps of the complex plane, and stochastic iterations of function systems are briefly explored for advanced students. The author also explores applications in mechanics, electromagnetism, celestial mechanics, nonlinear control theory, and macroeconomy. A set of problems consolidating the knowledge of the different subjects, including more elaborated exercises, are provided for all chapters. 410 0$aUNITEXT for Physics,$x2198-7890 606 $aChaotic behavior in systems 606 $aDynamics 615 0$aChaotic behavior in systems. 615 0$aDynamics. 676 $a003.857 700 $aDila?o$b Rui$01169698 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910686474803321 996 $aDynamical System and Chaos$93090678 997 $aUNINA