Fractals, Wavelets, and their Applications

Part I: Fractal Theory

- Introduction to Fractals

- Geometry of self similar sets

- An introduction to Julia and Fatou set

- Crazy topology in complex dynamics

- Measure preserving fractal homeomorphisms

- The dimension theory of almost self affine sets and measures

- Countable alphabet non autonomous self affine sets

- On transverse hyperplanes to self similar Jordan arcs

- Fractals in product fuzzy metric space

- Some properties on Koch curve

- Projections of Mandelbrot percolation in higher dimensions

- Some examples of finite type fractals in three dimensional space

- Fractals in partial metric spaces

Part II: Wavelet Theory

- Frames and extension problems I

- Frames and extension problems II

- Local fractal functions and function spaces

- Some istorical precedents of the fractal functions

- A new class of rational quadratic fractal function with positive shape preservation

- Interval wavelets determined by points on the circle

- Construction of multi scaling functions using matrix polynomials

- A remark on reconstruction of splines from their local weighted average samples

- C1rational cubic fractal interpolation surface using functional values

- On fractal rational functions

Part III: Applications of Fractals and Wavelets

- Innovation on the tortuous path: Fractal Electronics

- Permutation entropy analysis of EEG of mild cognitive impairment patients during memory activation task

- A multifractal based image analysis for cervical dysplasia classification

- Self similar network traffic modeling using fractal point process Markovian approach

- Validation of variance based fitting for self similar network traffic

- Self similar network traffic modeling using circulant Markov modulated poisson process

- Investigation of priority based optical packet switch under self similar variable length input traffic using matrix queuing theory

- Computationally efficient wavelet

Some key contributors and editors include Robert Devaney, Michael Barnsley, Christoph Bandt, M.Urbanski, Mark Pollicott, Peter Massopust who are the founders of fractals; Scott Sutherland, Jeff Geronimo who are the pioneers in the field of Complex Dynamics; Bin Han, Karoly Simon and Vladimir Protasov who are the experts in the area of Wavelets.