1978
DOI: 10.1137/0134013
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Computation of the Stability Condition for the Hopf Bifurcation of Diffeomorphisms on $\mathbb{R}^2 $

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Cited by 89 publications
(45 citation statements)
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“…The coefficient c 1 (a) can be computed directly using the formula below derived by Wan in the context of the Hopf bifurcation theory [27]. In [20] it is shown that when one uses area-preserving coordinate changes, this formula by Wan yields the twist coefficient τ 1 that is used to verify the non-degeneracy condition necessary to apply the KAM theorem.…”
Section: Im(λ) Re(λ)mentioning
confidence: 99%
“…The coefficient c 1 (a) can be computed directly using the formula below derived by Wan in the context of the Hopf bifurcation theory [27]. In [20] it is shown that when one uses area-preserving coordinate changes, this formula by Wan yields the twist coefficient τ 1 that is used to verify the non-degeneracy condition necessary to apply the KAM theorem.…”
Section: Im(λ) Re(λ)mentioning
confidence: 99%
“…First, the period ofthe cycle for values of r near the bifurcation point is always greater than 100 generations, and the cycle period increases as r is moved away from the point ofbifurcation. The period at the bifurcation point can be simply calculated from the imaginary part ofthe eigenvalues at the bifurcation point (7). The eigenvalues at the bifurcation point are ofthe form e" , and the period is 2Xr/@.…”
Section: Resultsmentioning
confidence: 99%
“…The coefficient c 1 can be computed directly using the formula below derived by Wan in the context of Hopf bifurcation theory [21]. In [22], it is shown that, when one uses area-preserving coordinate changes, Wan's formula yields the twist coefficient τ 1 that is used to verify the non-degeneracy condition necessary to apply the KAM theorem.…”
Section: Theorem 3 Assume That τ(ζζ)mentioning
confidence: 99%