Lecture Notes on Dynamical Systems Chaos And Fractal Geometry

Overview & Synopsis

Topics covered in
this notes include: The Orbits of One-Dimensional Maps, Bifurcation and the
Logistic Family, Sharkovsky�s Theorem, Metric Spaces, Devaney�s Definition
of Chaos, Conjugacy of Dynamical Systems, Singer�s Theorem, Fractals,
Newton�s Method, Iteration of Continuous Functions, Linear Transformation
and Transformations Induced by Linear Transformations, Some Elementary
Complex Dynamics, Examples of Substitutions, Compactness in Metric Spaces
and the Metric Properties of Substitutions, Substitution Dynamical Systems,
Sturmian Sequences and Irrational Rotations.