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)
Periodic orbits in k-symmetric dynamical systems. (English) Zbl 1194.37149
Summary: A map L is called k-symmetric if its kth iterate L k possesses more symmetry than L, for some value of k. In k-symmetric systems, there exists a notion of k-symmetric orbits. This paper deels with k-symmetric periodic orbits. We derive a relation between orbits that are k-symmetric with respect to reversing k-symmetries and symmetric orbits of L k . With this relation we set out an efficient method for finding systematically all periodic orbits that are k-symmetric with respect to reversing k-symmetries. This k-symmetric fixed set iteration (FSI) method generalizes a celebrated method due to DeVogelaere that applies to symmetric periodic orbits in reversible dynamical systems.We use the FSI method to study k-symmetric periodic orbits of a map of the plane 2 possessing a crystallographic reversing k-symmetry group. The explicit findings illustrate a typically k-symmetric phenomenon, consisting of a nontrivial relation between the symmetry properties of periodic orbits and their periods.
MSC:
37N05Dynamical systems in classical and celestial mechanics
70K99Nonlinear dynamics (general mechanics)