Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4669442 | Bulletin des Sciences Mathématiques | 2009 | 23 Pages |
We consider some analytic behaviors (convexity, monotonicity and number of critical points) of the period function of period annuli of the potential system and focus on the case when g(x) is a polynomial whose roots are all real. The main contributions of this paper are twofold: (i) analytic behaviors are given for the period functions of period annuli surrounding one or more and simple or degenerate equilibria; (ii) as a nontrivial application of the general conclusions in (i), a purely analytical and shorter proof is provided for a result for the case degg=4 recently obtained by Chengzhi Li and Kening Lu with some help of computer algebra [Chengzhi Li, Kening Lu, The period function of hyperelliptic Hamiltonian of degree 5 with real critical points, Nonlinearity 21 (2008) 465–483].