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A HIGHER DIMENSIONAL GENERALIZATION OF BENDIXON’S CRITERION
A. Pogromsky* G. Leonov** H. Nijmeijer*
* Department of Mechanical Engineering, Eindhoven University
of Technology, P.O. Box 513, 5600 MB, Eindhoven, The
Netherlands
{A.Pogromsky, H.Nijmeijer}@tue.nl
** Department of Mathematics and Mechanics,
St. Petersburg State University,
2, Bibliotechnaya pl., Petrodvorets, St. Petersburg, 198904, Russia
Leonov@math.lgu.spb.su
Conditions are given that guarantee the nonexistence of periodic orbits lying entirely in a simply connected set. The conditions are formulated in terms of matrix inequalities involving the variational equation. For systems defined in R2 the conditions are equivalent to Bendixon’s criterion. A connection with analytic estimates of the Hausdorff dimension of invariant compact sets is emphasized.
Keywords: linerization, periodic solutions, direct Lyapunov method
Session slot T-Mo-M08: Analysis of Nonlinear Systems/Area code 2c : Non-linear Systems
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