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Zbl 1084.34037
Sabatini, M.
Liénard limit cycles enclosing period annuli, or enclosed by period annuli.
(English)
[J] Rocky Mt. J. Math. 35, No. 1, 253-266 (2005). ISSN 0035-7596

The author constructs polynomial systems of differential equations on $\Bbb{R}^2$ of the form $$\text{(L)}\quad \dot x = y, \ \dot y = -g(x) -yf(x),$$ of two types: (1) the system is of degree $4k+2$ and has a period annulus (an annular region composed of periodic orbits) that surrounds $2k$ limit cycles (isolated closed orbits); (2) the system is of degree $6k$ and has $k$ concentric limit cycles surrounding a center (a period annulus whose inner boundary is an equilibrium point). The author also proves existence of a real analytic system of the form (L) containing a center surrounded by infinitely many limit cycles.
[Douglas S. Shafer (Charlotte)]
MSC 2000:
*34C05 Qualitative theory of some special solutions of ODE
34C07 Theory of limit cycles of polynomial and analytic vector fields

Keywords: Liénard; limit cycle; period annulus

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