TY  - BOOK
AU  - McCauley,Joseph L.
TI  - Chaos, dynamics, and fractals: an algorithmic approach to deterministic chaos 
T2  - Cambridge nonlinear science series
SN  - 9780511564154 (ebook)
AV  - QC174.17.C45 M33 1993
U1  - 516.15 19
PY  - 1993///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Deterministic chaos
KW  - Algorithms
KW  - Mappings (Mathematics)
KW  - Fractals
KW  - Mathematical physics
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015)
N2  - This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal critical exponents, devil's staircases and the Farey tree. The author uses a fully discrete method, a 'theoretical computer arithmetic', because finite (but not fixed) precision cannot be avoided in computation or experiment. This leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The connection is made with Turing's ideas of computable numbers and it is explained why the continuum approach leads to predictions that are not necessarily realized in computation or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed
UR  - https://doi.org/10.1017/CBO9780511564154
ER  -