Chaos, dynamics, and fractals : an algorithmic approach to deterministic chaos

摘要: This book develops deterministic chaos and fractals from the standpoint of iterated maps, but emphasis makes it very different all other books in field. It provides reader with an introduction to more recent developments, such as weak universality, multifractals, shadowing, well older subjects like universal critical exponents, devil's staircases Farey tree. The author uses a fully discrete method, 'theoretical computer arithmetic', because finite (but not fixed) precision cannot be avoided computation or experiment. leads general formulation terms symbolic dynamics idea universality. connection is made Turing's ideas computable numbers explained why continuum approach predictions that are necessarily realized nature, whereas yields possible histograms can observed computed.