61. Dynamical Systems And Normal Forms A dynamical system is a description of the deterministic evolution of a state variable, whihc may be a finite or an infinite dimensional object. http://modelmath.mcmaster.ca/areas/dynamical_systems.htm

Dynamical systems and Normal forms A dynamical system is a description of the deterministic evolution of a state variable, whihc may be a finite or an infinite dimensional object. Typically, a dynamical system is given as the flow of a vector field, or the solution of a differential or a difference equation. Many examples of dynamical systems arise in physical or engineering sciences and in biological or medical applications. Specific systems under study by members of the AIMS Laboratory include waves in nonlinear optics, atmospheric vortices, and surface and internal waves in the ocean, among many others. Modeling of physical systems by a dynamical system can be either over finite dimensional phase space, the continuum, or on discrete lattices. Due to the energy conservative nature of many of the problems of interest to AIMS Lab members, it is quite common to work with Hamiltonian dynamical systems in particular. Among the numerous analytical and numerical techniques available in the field of dynamical systems, a classical point of view advocates an initial normal forms analysis. Under transformation, a mathematician seeks to reduce a nonlinear dynamical system to its simplest form, eliminating inessential nonlinearities or degrees of freedom. In the context of Hamiltonian systems this technique is in particular very valuable in perturbation theory of invariant tori, in Nekhoroshev stability theory, in a Hamiltonian version of multiple scales analysis for partial differential equations, and in the renormalization process by which nonlinear wave turbulence can be understood.

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70. Technische Universiteit Eindhoven: Dynamical Systems Top of this page Skip navigation, go straight to the content Technische Universiteit Eindhoven Inloggen TU/e A tot Z FAQ http://w3.ele.tue.nl/nl/mbs/cs/education/courses/dynamical_systems/

Top of this page Skip navigation, go straight to the content Technische Universiteit Eindhoven Inloggen TU/e A tot Z ... BIB Faculteit Elektrotechniek TU/e Faculteiten ELE MBS ... DISC Course on Linear Matrix Inequalities in Control Course Dynamical Systems Studiewijzer corresponding page owinfo 1. General course information Course: "Dynamical Systems", Code: 5MX00 Credit: 3 ECTS Meant for: EIT (4th year) MEIT (1st year): Master Electrical Engineering, Master Sustainable Energy Technology and Master Systems and Control Classes: Semester 1 2007, Block A and block B Lectures on Thursdays, 8.45-10.30. All classes are held in Room PT 1.05 Lecturer: Name: Dr. Siep Weiland Email: s.weiland@tue.nl Office: E-Hoog-4.35 Phone: 040.247.5979 or 040.247.2300 (secr.) 2. Aims and scope Global analysis of nonlinear dynamical systems, which occur in electrical engineering such as electrical networks (power engineering, electrical machines) oscillators, lasers, neural networks and nonlinear processes. We treat specific topics such as periodic, quasi-periodic and chaotic systems. Existence and uniqueness of solutions of (nonlinear) differential equations. Fixed points, limit sets, periodic orbits, Lyapunov functions and stability, Bendixson theorem, Poincare maps, bifurcation. Chaotic attractors, Lyapunov exponents, iteration of functions and periodic points. 3. Material and Schedule

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