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  • Critical periods of perturbations of reversible rigidly isochronous centers
    Chen, Xingwu ; Romanovski, Valery ; Zhang, Weinian
    In this paper we discuss bifurcation of critical periods in an m-th degree time-reversible system, which is a perturbation of an n-th degree homogeneous vector field with a rigidly isochronous center ... at the origin. We present period-bifurcation functions as integrals of analytic functions which depend on perturbation coefficients and reduce the problem of critical periods to finding zeros of a judging function. This procedure gives not only the number of critical periods bifurcating from the period annulus but also the location of these critical periods. Applying our procedure to the case n=m=2 we determine the maximum number of critical periods and their location; to the case n=m=3 we investigate the bifurcation of critical periods up to the first order in ▫$\epsilon$▫ and obtain the expression of the second period-bifurcation function when the first one vanishes.
    Vir: Journal of differential equations. - ISSN 0022-0396 (Vol. 251, iss. 6, 2011, str. 1505-1525)
    Vrsta gradiva - članek, sestavni del
    Leto - 2011
    Jezik - angleški
    COBISS.SI-ID - 18500360

vir: Journal of differential equations. - ISSN 0022-0396 (Vol. 251, iss. 6, 2011, str. 1505-1525)

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