Introduction to Dynamical Systems and Chaos – course plan

Imre Péter Tóth, fall 2005

• course instructor:

– name: Imre Péter Tóth

– home phone number: (06) 20/537-22-56 (mornings, evenings)

– office: Rényi Institute of Mathematics, room 110 (address: V. district, Reáltanoda u. 13-15 (near the subway stations ‘Astoria’ and ‘Ferenciek Tere’)

– e-mail: mogy@renyi.hu (the easiest way to contact)

• book used: Kathleen T. Alligood, Tim D. Sauer, James A. Yorke: Chaos – An Introduction to Dynamical Systems; Springer, 1996

• planned topics:

– one-dimensional and two-dimanesional maps as dynamical systems

– limit sets and recurrence

– chaos and Lyapunov exponents

– symbolic dynamics, Smale horseshoe

– fractals and fractal (box counting) dimension

– differentioal equations as dynamical systems; limit sets and recurrence

– Lorenz attractor

– bifurcations

• things you will need to know:

– calculus:

∗ limits

∗ differentiation, differentiation of functions in several variables

∗ continuity, open/closed sets

– linear algebra:

∗ Euclidean space

∗ matrix of a linear mapping

∗ eigenvalues, eigenvectors of a linear mapping; canonical form

• Evaluation will be based on weekly homeworks (40% of all points), a written midterm exam (20%) and a written final exam (40%).

I intend to illustrate the material with as many examples of applications as possible. Those who are interested can have exercises requiring computer simulation both for homework and midterm.