NOC:Chaotic Dynamical Systems


Lecture 1 - The beginning


Lecture 2 - Elementary Concepts


Lecture 3 - Elementary Concepts (Continued...)


Lecture 4 - More on orbits


Lecture 5 - Peiods of Periodic Points


Lecture 6 - Scrambled Sets


Lecture 7 - Sensitive Dependence on Initial Conditions


Lecture 8 - A Population Dynamics Model


Lecture 9 - Bifurcations


Lecture 10 - Nonlinear Systems


Lecture 11 - Horseshoe Attractor


Lecture 12 - Dynamics of the Horseshoe Attractor


Lecture 13 - Recurrence


Lecture 14 - Recurrence (Continued...)


Lecture 15 - Transitivity


Lecture 16 - Devaney’s Chaos


Lecture 17 - Transitivity = Chaos on Intervals


Lecture 18 - Stronger forms of Transitivity


Lecture 19 - Chaotic Properties of Mixing Systems


Lecture 20 - Weakly Mixing and Chaos


Lecture 21 - Strongly Transitive Systems


Lecture 22 - Strongly Transitive Systems (Continued...)


Lecture 23 - Introduction to Symbolic Dynamics


Lecture 24 - Shift Spaces


Lecture 25 - Subshifts of Finite Type


Lecture 26 - Subshifts of Finite Type (Continued...), Chatoic Dynamical Systems


Lecture 27 - Measuring Chaos - Topological Entropy


Lecture 28 - Topological Entropy - Adler’s Version


Lecture 29 - Bowen’s Definition of Topological Entropy


Lecture 30 - Equivalance of the two definitions of Topological Entropy


Lecture 31 - Linear Systems in Two Dimentions


Lecture 32 - Asymptotic Properties of Orbits of Linear Transformation in IR2


Lecture 33 - Hyperbolic Toral Automorphisms


Lecture 34 - Chaos in Toral Automorphisms


Lecture 35 - Chaotic Attractors of Henon Maps