Dynamic Equations [ Back ]

Dates:
15.09.01 - 31.05.02
Place:
Universitat Autònoma de Barcelona
Address:
Department of Economics
Teacher:
Xavier Jarque

Program:
  1. Discrete dynamical systems. Iteration of functions. Examples and preliminaries. Iteration. Notion of orbit. Periodic points. Hyperbolicity and typical bifurcations. The quadratic family. Symbolic dynamics. Notion of (Devaney's) chaos.
  2. Continuous dynamical systems. Differential equations. Examples and preliminaries. Classification. Existence and uniqueness Theorem. The phase portrait of autonomous differential equations. Singular points and periodic orbits. Stability and Liapunov functions. Hyperbolic singular points. Limit cycles and the Poincaré map.


References:
  1. K.T. Alligood, T.D. Sauer and J.A. Yorke "Chaos. An introduction to dynamical systems", Springer-Verlag.
  2. R. L. Devaney "An introduction to chaotic dynamical systems", Benjamin/cummings Pub.
  3. L. Perko, "Differential equations and dynamical systems", Springer-Verlag