I would like to learn seriously the mandelbrot set. The idea is to handle it well enough to see why proving its locally connectedness is so difficult. Can you suggest me some books/PDF online? I know complex analysis but almost nothing about complex dynamics and fractals.
Looking around it seems that this subject arises in many different areas. I would like to know a reasonable order of the argument to study, to optimize my learning process instead of searching randomly on the web.
Start with the classic books: The Beauty of Fractals and The Science of Fractal Images.