Dynamic Systems Applied

Basic information

Workload: 

45 hours

Prerequisite: 

Functional Analysis: Fundamentals

Syllabus: 

Dynamic systems with discrete and continuous time. Trajectories, fixed points, periodic orbits, flow, attractors. Equivalence and conjugation of vector fields. Tubular flow theorem. Classification of linear flows. Lyapunov's stability and functions. Convergence and invariant sets. Global properties. Hyperbolicity. Invariant varieties. Bifurcation. Balance and linearization. Hartman-Grobman theorem. Hamiltonian and conservative systems. Symplectic maps. Numerical methods like dynamic systems. Introduction to the dynamics of stochastic systems. Application to real models. 

Bibliography

Mandatory: 

  • Stuart e Humphries (1996) Dynamical Systems and Numerical Analysis. Cambridge
  • Hasselblatt B; Katok A (2012) A First Course in Dynamics. Cambridge University Press
  • Hirsch, M;  Smale, S; Devaney, R (2013) Differential Equations, dynamical systems and an introduction to chaos. (Third Edition). Elsevier.
     

Complementary: 

  • Duan (2015). An Introduction to Stochastic Dynamics. Cambridge.
  • Devaney (2003) An Introduction to Chaotic Dynamical Systems. CRC Press.
  • Hirsch, M;  Smale, S; Devaney, R (2013) Differential Equations, dynamical systems and an introduction to chaos. (Third Edition). Elsevier.
  • Guckenheimer J, Holmes P (2002) Nonlinear oscillators, Dynamical systems and Bifurcations of Vector fields. Springer.
  • Perko, L (2001) Differential Equations and dynamical systems. TAM. Springer.