Chaos, Dynamics, and Fractals. An Algorithmic Approach to Deterministic Chaos

MCCAULEY, Joseph L.

ISBN 10: 0521416582 / ISBN 13: 9780521416580

Edité par Cambridge University Press, Cambridge, 1993

A propos de cet article

xiii + 323 p. [Cambridge Nonlinear Science Series ; 2]. N° de réf. du vendeur 015583

Détails bibliographiques

Titre : Chaos, Dynamics, and Fractals. An ...

Éditeur : Cambridge University Press, Cambridge

Date d'édition : 1993

Reliure : Hardcover

Etat : Very Good

Etat de la jaquette : Very Good

Edition : 1st Edition

A propos de ce titre

Synopsis :

The author presents deterministic chaos from the standpoint of theoretical computer arithmetic, leading to universal properties described by symbolic dynamics.

Présentation de l'éditeur:

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.