Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0841.58036
Brin, M.; Pesin, Ya.
On Morse-Smale endomorphisms. (English)
[A] 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). ISBN 0-8218-0456-1/hbk

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.

MSC 2000:: *37D15 Morse-Smale systems

Keywords: transversality; pseudo-orbits; unstable manifolds; stable manifold; Morse-Smale endomorphism

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]