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, |
Reference Books:
- Mandelbrot B. Fractal Geometry of Nature, W.H. Freeman and Company
- Barnsley M. F. Fractals Everywhere, Academic Press
- Mattila. Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability, Cambridge University Press
- Peitgen, Jurgens and Saupe, Chaos and Fractals, New Frontiers
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