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)
On Morse-Smale endomorphisms. (English) Zbl 0841.58036
Bunimovich, L. A. (ed.) et al., Sinai’s Moscow seminar on dynamical systems. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 171, 35-43 (1996).
Summary: A $C^1$-map $f$ of a compact manifold $M$ is a Morse-Smale endomorphism if the nonwandering set of $f$ is finite and hyperbolic and the local stable and global unstable manifolds of periodic points intersect transversally. Morse-Smale endomorphisms appear naturally in the dynamics of the evolution operator on the set of traveling wave solutions for lattice models of unbounded media. The main result of this paper is the openness of the set of Morse-Smale endomorphisms in the space $C^1 (M, M)$ of $C^1$-maps of $M$ into itself. The usual order relation on $f$ (given by the intersections of local stable and global unstable manifolds) is used to describe the orbit structure of $f$ and its small $C^1$-perturbations. For the entire collection see [Zbl 0831.00008].

MSC:
 37D15 Morse-Smale systems