Introduction to dynamical systems – Analytical and numerical methods – The Mathematica software
Analytical and numerical solution of differential equations – Computing solutions using Mathematica
General concepts of dynamical systems – Trajectories, phase space
Conservative dynamical systems with one degree of freedom
Two-dimensional autonomous linear systems
Two-dimensional autonomous nonlinear systems
Bifurcations and limit cycles
One-dimensional and two-dimensional maps
Chaotic maps and symbolic dynamics
Applications
Non-autonomous systems with one degree of freedom – Oscillators
Periodic, quasiperiodic, and chaotic oscillations
Limit cycles and strange attractors in the Duffing equation
The displacement map, the logistic map, and the Hénon map