Chaotische Dynamical Systems

Vrije Universiteit Amsterdam

Course Description

  • Course Name

    Chaotische Dynamical Systems

  • Host University

    Vrije Universiteit Amsterdam

  • Location

    Amsterdam, The Netherlands

  • Area of Study

    Geometry, Mathematics

  • Language Level

    Taught In English

  • Course Level Recommendations

    Upper

    ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

    Hours & Credits

  • ECTS Credits

    6
  • Recommended U.S. Semester Credits
    3
  • Recommended U.S. Quarter Units
    4
  • Overview

    COURSE OBJECTIVE
    After this course, the student

    • has a basic knowledge of nonlinear dynamical systems.
    • understands the mechanisms that cause chaos in 1-dimensional maps and is able to investigate these maps.
    • understands mechanisms that cause chaos in 2-dimensional maps and is able to apply techniques to investigate these maps.
    • is able to compute and recognize important nonlinear bifurcations and appreciates their importance for dynamics.
    • has used the theory of dynamical systems in an application, and has communicated his experience to his/her peers.

     

    COURSE CONTENT
    Modern dynamical systems theory originates with the work of Poincare, who revolutionized the study of dynamical systems by introducing qualitative techniques of geometry and topology to discuss global properties of solutions. The study of chaotic dynamical systems from the 1960s on lead to a breakthrough in science and an explosion of interest in the field of dynamical systems.

    This course investigates nonlinear dynamical systems and explains basic ideas of the field in low dimensional settings of iterated maps on the line and in the plane. Important results and ideas are explained in this context, such as symbolic dynamics, "period three implies chaos", period doubling route to chaos, the Smale horseshoe map and bifurcations of periodic points.

    TEACHING METHODS
    Lectures, tutorials and a group project

    TYPE OF ASSESSMENT
    Exams and a group project

Course Disclaimer

Courses and course hours of instruction are subject to change.

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