Subject Code: MA7L004 Subject Name:  Fractals L-T-P: 3-1-0 Credit:4
Pre-requisite(s): Real Analysis (MA5L002)
The philosophy and scope of fractal geometry, Scaling and self similarity, Hausdorff measure and dimensions, Box-counting dimensions, Techniques for calculating dimensions, Local structure and projections of fractals, The Thermodynamic Formalism: Pressure and Gibb’s measures, the dimension formula, Invariant measuresand the transfer operator, Entropy and the Variational principle;  The ergodic theorem; The renewal theorem;  Martingales and the convergence theorem, Bi-Lipschitz equivalence of fractals; Multifractal Analysis; Applications of fractals: Iterated function systems (IFS) and Recurrent IFS, Applications to image compression, Julia sets and the Mandelbrot set, Random fractals, Brownian motion and Random walks, Percolation, Fractal interpolation,
Text Books:
  1. Falconer K. Fractal Geometry: Mathematical Foundations and Applications,  John Wiley & Sons.
  2. Falconer K. Techniques in Fractal Geometry,  John Wiley & Sons.
Reference Books:
  1. Mandelbrot B.  Fractal Geometry of Nature, W.H. Freeman and Company
  2. Barnsley M. F.  Fractals Everywhere,  Academic Press
  3. Mattila. Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability, Cambridge University Press
  4. Peitgen, Jurgens and Saupe, Chaos and Fractals, New Frontiers