Vol. 17, No. 2, 1966

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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