Vol. 35, No. 1, 1970

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Transversally perturbed planar dynamical systems

Roger McCann

Vol. 35 (1970), No. 1, 187–194

This paper investigates the behavior of limit cycles of a planar dynamical system which has been perturbed transversally. In particular, it is shown that if C is a limit cycle of the unperturbed dynamical system, then there are limit cycles of the perturbed dynamical systems arbitrarily close to C. Also, if C is an exterior Iimit cycle of the unperturbed dynamical system, then there is an outer neighborhood of C which consists solely of cycles of the perlurbed dynamical systems.

Mathematical Subject Classification
Primary: 54.82
Secondary: 34.00
Received: 22 December 1969
Published: 1 October 1970
Roger McCann