On the Quantitative Estimates of the Remainder in Normal Forms
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چکیده
We consider an analytic Hamiltonian system with three degrees of freedom and having a family of periodic orbits with a transition stability complex instability We reduce the Hamiltonian to a normal form around a transition periodic orbit and we obtain H Z r R r The analysis of the truncated normal form Z r allows the description of a Hopf bifurcation of D tori However this communication will concentrate on the study of the remainder R r and some comparison between the remainder obtained when considering the normal form around an elliptic equilib rium point and around a critical periodic orbit will be made
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تاریخ انتشار 2007