SUBJECT
Nonlinear dynamics and chaos
lecture
master
3
Semester 2
Spring semester
The different types of dynamical systems, nonlinearity, examples from physics, chemistry, biology and engineering, respectively. One dimensional maps, dynamics on the circle, nonlinear oscillators, damped pendulums, Josephson junctions in superconductivity. Two-dimensional dynamics, Poincaré-crosssection, classifications of linear systems, linearization around the fixed points, conservative and reversible systems, index theorems. Limit cycles: Poincaré-Bendixson theorem, relaxations in oscillations. Classification of bifurcations, catastrophes. Chaos: Lorenz-equations, strange attractors, chaos in one dimensional maps, Lyapunov exponents, universality, fractal dimensions, multifractal descriptions.
required readings:
Tamás Tél, Márton Gruiz, Chaotic Dynamics: An Introduction Based on Classical Mechanics, Cambridge University Press, 2006.
recommended readings:
Steven Srogatz: Nonlinear Dynamics and Chaos (Westview Press, 2001)