Dynamics of nonlinear &
chaotic systems Lecture 1: An
Introduction
S. Denisov
Dynamics of nonlinear & chaotic systems
Lecture 1: An Introduction
S. Denisov
Theo I, Institut f¨ur Physik, Universit¨at Augsburg
Introduction S. Denisov
My name: Sergey ([Sjergjej]) Denisov
My location: IFP, South Building, Room 517, phone: 3228; Q
& A: every working day, better afternoon
My email: sergey.denisov@physik.uni-augsburg.de
My web-page: http://www.physik.uni-augsburg.de/ denisose
Dynamics of nonlinear &
chaotic systems Lecture 1: An
Introduction S. Denisov
About the course
Course description
The course is aimed at newcomers to nonlinear dynamics and chaos, especially master students taking a FIRST course in this subject. The goal is to introduce the basic phenomena
observed in nonliear dynamics, explaining the mathematics involved in generating these phenomena, and showing how they can be used to understand some of the wonders of real world.
Introduction S. Denisov
The essential prerequisite is single-variable calculus, including curve-sketching, Taylor series, and basics of differential equations. In a few places, multivariable calculus (partial derivatives, Jacobian matrix, etc) and linear algebra
(eigenvalues & eigenvectors) are used (but I will remind/briefly introduce them). Basic physics (Newton laws etc) is used throughout.
Technical details
We will study problems which either demand (i) a piece of paper & a pen or (ii) a PC or laptop. The computer exercises will usually use Fortran, but you are free to use whatever
Dynamics of nonlinear &
chaotic systems Lecture 1: An
Introduction S. Denisov
About the course
Textbooks & sources:
Scholarpedia (http://www.scholarpedia.org) & Wiki (sometimes);
Edward Ott, Chaos in Dynamical Systems (the best to my taste);
Steven Strogatz, Nonlinear Dynamics and Chaos; http://www.physik.uni-
augsburg.de/ denisose/lecture.shtml
Introduction
S. Denisov Course outline
Dynamics: Nonlinear maps and chaos;
Dynamics: Nonlinear diff. equations & flows;
Geometry: strange attractors & fractals;
Dynamics: Hamiltonian chaos;
Dynamics: Control of chaos;
Quantum: Quantum chaos;
Real life: Chaos in our lives;
Dynamics of nonlinear &
chaotic systems Lecture 1: An
Introduction S. Denisov
About the course
Chaos logo & mascot: Lorenz attractor
Introduction S. Denisov
Dynamics of nonlinear &
chaotic systems Lecture 1: An
Introduction S. Denisov
