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Dynamical Systems I
This course deals with basic properties of solutions of ordinary Differential equations and Dynamical systems such as stability of equilibrium point, periodic orbits, etc. Course outlines are as follows:
Outline of the course
1.,Linear systems, Geometry of solutions, Bifurcations in linear systems, Linearized stability, Hartman-Grobman theorem, Liapunov Functions, Lassalle invariance principle
2. Autonomous systems in n dimension, Existence and uniqueness, Geometry of flows, Equivalence of flows, Elementary bifurcations
3. Periodic orbits, Limit cycles and separatrix cycles, Poincare map, Flouque Theory, The Poincare-Bendixson theorem, Stability of periodic orbits, Local bifurcations of periodic orbits.
4. Bifurcation of equilibria and periodic orbits in n-dimensional systems, Center manifold theorems, Center manifolds in parameter-dependent systems. Birkhoff normal forms.
5. Second order Hamiltonian and gradient systems, and their Bifurcations.
References:
1. Hirsch, W.M., Smale, S., Devaney, R., Differential Equations, Dynamical Systems and an Introduction to Chaos, Elsevior, 2004.
2. Hale, J., Kocak, H.; Dynamics and Bifurcations, Springer-Verlag, New York, 1991.
3. Perko, L., Differntial Equations and Dynamical systems, Third Edition, Springer-Verlag , 2001.
4. Guckenheimer, J.; Holmes, P.; Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York, 1988.
5. Wiggins, S.; Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, NewYork, 1990.
Elementary Differential equations, Linear Algebra, Mathematical Analysis
Midterm Exam: 40%,
Exam date, time and place: 1393/8/27, 9-12am, conference room
Final exam: 60%
Class hours: S-M, 03:00-05:00 PM, Classroom # 8
Office hour: with appoinment