Lecture 1 (Oct 6th)
Introduction. Discrete dynamical systems. Autonomous and non
autonomous case. Cycles. Simple examples, both 1D and 2D. Relation
between dimensionality and order of the system.
Lecture 2 (Oct 7th)
Solution
formula for the linear 1D case: homogeneous and non-homogeneous case. Example of amortization. Exercises. Equilibrium points. Examples of equilibrium points.
Lecture 3 (Oct 13th)
Definitions of stability, asymptotic stability, global
stability. Conditions for stability for a linear 1D fisrt-order
equation. Cobweb diagram. Linearization criterion for the 1D case.
Cobweb diagram with GeoGebra.
Lecture 4 (Oct 14th)
Stability criterion: the case of derivative equal to 1 or
-1. Examples. Cobweb Theorem of Economics. Models with expected price.
Lecture 5 (Oct 20th)
Linear discrete dynamical systems. Conditions for
equilibrium. Determinant of a matrix. Eigenvalues of a matrix. Spectral radius.
Stability criterion for linear systems.
Lecture 6 (Oct 21st)
Jury's criterion in dimensions 2 and 3. Examples.
Jacobian matrix. Linearization theorem and idea of the proof. Exercises from the written tests.