Fractals and Chaos

Code: MA564 | L-T-P-C: 3-0-0-6

Fractals: Cantor set, Sierpinski triangle, Von Koch curve, Hilbert and Peano curves, Weierstrass function. Self-similarity, Scaling, Similarity dimension, Box-counting dimension, Information dimension, Capacity dimension. Foundations of iterated function systems (IFS), Classical fractals generated by IFS, Contractions mapping principle, Collage theorem, some applications of Fractals.

Chaos: One dimensional maps, periodic points, sensitive dependence on initial conditions, chaos, Sarkoviskii theorem, Logistic map, Henon map. Dynamics of complex polynomials, Julia sets, Fatou sets, Mandelbrot set, characterization of Julia sets. Dynamics of Newton method.

Texts:

1. M. F. Barnsley, Fractals Everywhere, Second Edition, Academic Press, 1995.
2. R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Second Edition, Addision-Wesley, 1989.

References:

1. K. Falconer, Fractal Geometry – Mathematical Foundations and Applications, Third Edition, Wiley, 2013.