zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Chaotic evolution and strange attractors. The statistical analysis of time series for deterministic nonlinear systems. Notes prepared by Stefano Isola from the ‘Lezioni Lincee’ (Rome, May 1987). (English) Zbl 0683.58001
Lezioni Lincee. Cambridge etc.: Cambridge University Press. xi, 96 p. £25.00/hbk; $ 39.50/hbk; £8.95/pbk; $ 12.95/pbk (1989).
This book is a review on those aspects of dynamical systems which are more closely related with ergodic theory, namely with the study of the properties of the invariant measures generated by the time evolution themselves. The text is divided into two parts. The concept of the chaos for deterministic systems through a survey of some “historical topics” is developed in part one, like, for example, the interpolation of hydrodynamical turbulence. Some definitions of geometrical notions related to chaotic phenomena, like those of strange attractors, fractal dimensions, reconstruction of the dynamics from a time series and so on, are also given. In the second part the concept of invariant probability measure is introduced, along with some ergodic quantities such as characteristic exponents, entropy, dimensions, resonancy, etc. Also, a number of examples and figures in such a way as to give some references useful both as clarifying elements and to emphasize the deep mathematical ideas which permeate the theory of differential dynamical systems are considered. The book is an excellent introduction in chaotic evolution systems and strange attractors; for a broad audience of graduate students and faculty members.
Reviewer: L.G.Vulkov

MSC:
58-02Research monographs (global analysis)
37A99Ergodic theory
37D45Strange attractors, chaotic dynamics