Hyperbolic sets for noninvertible maps and relations

Pages: 339 - 357, Volume 5, Issue 2, April 1999

doi:10.3934/dcds.1999.5.339       Abstract        Full Text (330.6K)       Related Articles

Evelyn Sander - Department of Mathematical Sciences, George Mason University, MS 3F2, 4400 University Drive, Fairfax, VA 22030, United States (email)

Abstract: This paper develops the theory of hyperbolic sets for relations, a generalization of both noninvertible and multivalued maps. We give proofs of shadowing and the stable manifold theorem in this context.

Keywords:  Dynamical systems, iteration, hyperbolic sets, invariant manifolds, shadowing, relations, noninvertible maps, multivalued maps.
Mathematics Subject Classification:  58F.

Received: September 1997;      Revised: November 1998;      Published: January 1999.