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|Title: ||Perturbations from an elliptic Hamiltonian of degree four - II. Cuspidal loop|
|Authors: ||DUMORTIER, Freddy|
|Issue Date: ||2001|
|Publisher: ||ACADEMIC PRESS INC|
|Citation: ||Journal of differential equations, 175(2). p. 209-243|
|Abstract: ||The paper deals with Lienard equations of the form x = y, y = P(x) + yQ(x) with P and Q polynomials of degree respectively 3 and 2. Attention goes to perturbations of the Hamiltonian vector field with an elliptic Hamiltonian of degree 4, exhibiting a cuspidal loop. It is proven that the least upper bound for the number of zeros of the related elliptic integral is four, and this upper bound is a sharp one. This permits to prove the existence of Lienard equations of type (3, 2) with at least four limit cycles. The paper also contains a complete result on the respective number of "small" and "large" limit cycles|
|ISI #: ||000171278800002|
|Type: ||Journal Contribution|
|Validation: ||ecoom, 2002|
|Appears in Collections: ||Research publications|
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