1978
DOI: 10.1016/0022-247x(78)90120-8
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Bifurcation formulae derived from center manifold theory

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Cited by 149 publications
(71 citation statements)
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“…It should be noticed that the above Υ is exactly the one derived by Hassard and Wan [10] by using center manifold reduction and normal form approach (for more details, see [7]). …”
Section: G(z α β) := P B(zq + Zq α β)supporting
confidence: 56%
See 1 more Smart Citation
“…It should be noticed that the above Υ is exactly the one derived by Hassard and Wan [10] by using center manifold reduction and normal form approach (for more details, see [7]). …”
Section: G(z α β) := P B(zq + Zq α β)supporting
confidence: 56%
“…In the standard Hopf bifurcation theory ( [9,10,13]), the central hypothesis is that at the critical value of the bifurcation parameter the infinitesimal generator has a complex conjugate pair of simple purely imaginary eigenvalues. The presence of symmetry may cause purely imaginary eigenvalues to arise with higher multiplicities, which causes the bifurcation problem to become more complicated; see for instance [6].…”
Section: ) Is Invariant Under the Transformation (X T) → ( (γ) T) mentioning
confidence: 99%
“…Although theoretically the isochronous center problem can be solved by letting all period constants be zero, it is not the fact in practice which is due to the difficulty of computing the period constants. Questions relating to calculation of period constants have been studied by a number of authors (See [7,8,10,11]). However, only the first few ones can be given.…”
Section: Introductionmentioning
confidence: 99%
“…where the /" are homogeneous polynomials of degree n, and then equating corresponding powers of ux we obtain a unique formal Taylor expansion of a; for a discussion of this procedure as well as the numerical implementation, see [15,16,23]. The number N can be taken as high as the differentiability of nt permits (i = 1,2).…”
mentioning
confidence: 99%
“…If we define the sequence of numbers km(m > 0) by (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) km = f~2\in^g2{r2(r, pj) dr, then (7.19) leads to…”
mentioning
confidence: 99%