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)
Dynamics of piecewise isometries. (English) Zbl 0964.37009

The subject of the paper is Euclidean piecewise isometric dynamical systems (p.i.d.s.). A piecewise isometry is a pair (T,𝒫), where T:XX is a map such that its restriction to P i , i=0,,r-1 is a Euclidean isometry. Here X is a subset of N and 𝒫={P 0 ,,P r-1 } (r>1) is a finite partition of X. Such systems are direct generalization of interval exchange transformations to non-invertible, higher-dimensional maps.

Considering geometrical properties of p.i.d.s. and symbolic dynamics the author describes the relation between the growth of the associated semigroup of isometries and the growth of symbolic words. The notion of entropy for piecewise isometry is introduced and expressed in terms of the growth of symbolic words. Furthermore, the author studies necessary conditions for a p.i.d.s. to generate all possible finite words. Finally, some remarks on the interplay between symbolic codings, periodic points, and the geometry of cells (i.e. sets following the same coding pattern) are given. A number of results included are generalizations of results for interval exchangers.

MSC:
37B10Symbolic dynamics
37B40Topological entropy
37F99Complex dynamical systems
52A07Convex sets in topological vector spaces (convex geometry)