BIZARRE TOPOLOGY IS NATURAL IN DYNAMICAL-SYSTEMS

Authors
KENNEDY JA YORKE JA
Citation
Ja. Kennedy et Ja. Yorke, BIZARRE TOPOLOGY IS NATURAL IN DYNAMICAL-SYSTEMS, Bulletin, new series, of the American Mathematical Society, 32(3), 1995, pp. 309-316
Citations number
13
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Bulletin, new series, of the American Mathematical Society → ACNP
ISSN journal
02730979
Volume
32
Issue
3
Year of publication
1995
Pages
309 - 316
Database
ISI
SICI code
0273-0979(1995)32:3<309:BTINID>2.0.ZU;2-H
Abstract
We describe an example of a C(infinity) diffeomorphism on a 7-manifold which has a compact invariant set such that uncountably many of its c onnected components are pseudocircles. (Any 7-manifold will suffice.) Furthermore, any diffeomorphism which is sufficiently close (in the C1 metric) to the constructed map has a similar invariant set, and the d ynamics of the map on the invariant set are chaotic.