NPTEL : NOC:Chaotic Dynamical Systems (Mathematics)

Co-ordinators : Dr. Anima Nagar


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