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Applied Dynamical Systems I
ME215A, Fall Quarter 2010

Meets: Monday, Wednesday 11:00-12:15 Girvetz 2110

Course Description:

This course will cover dynamical systems theory, and the application of dynamical systems techniques to mathematical, physical, biological, and technological systems described by ordinary differential equations or maps. The primary focus will be on dissipative systems, so that the course is complementary to the Advanced Dynamics sequence (ME 201 and 202) which primarily focusses on conservative systems.

Specific topics to be covered include:

  • fixed points for vector fields and maps, and their stability properties
  • Liapunov functions
  • invariant manifolds for linear and nonlinear systems
  • periodic orbits
  • index theory
  • asymptotic behavior, attractors
  • Poincare-Bendixson Theorem
  • Poincare maps
  • structural stability
  • center manifolds
  • normal forms
  • bifurcations of fixed points of vector fields
  • bifurcations of fixed points of maps
  • Takens-Bogdanov bifurcation
  • Melnikov's method
  • the Smale horseshoe
  • symbolic dynamics
  • chaos and strange attractors
    Questions? Email Jeff Moehlis at moehlis@engineering.ucsb.edu

    Course Syllabus

    Homework