Vol. 17, No. 2, 1966

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 311: 1
Vol. 310: 1  2
Vol. 309: 1  2
Vol. 308: 1  2
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
Existence of half-trajectories in prescribed regions and asymptotic orbital stability

Wallace E. Johnson

Vol. 17 (1966), No. 2, 243–248

A theorem is proved concerning the existence of a half-trajectory in the neighborhood of a semi-invariant set of a general dynamical system. A corollary of this theorem strengthens a result of P. Mendelson. The theorem is further used to obtain a necessary and sufficient condition for a compact positively invariant set to be positively asymptotically orbitally stable, and the condition is compared with another one due to S. Lefschetz.

Mathematical Subject Classification
Primary: 34.51
Received: 7 December 1964
Published: 1 May 1966
Wallace E. Johnson