New lower bounds of the number of critical periods in reversible centers
The main objective of this paper is to find the highest possible lower bound for the maximum number \(C_l(n)\) of local critical periods that can bifurcate from an \(n\)-th degree planar time-reversible system. This problem is completely solved only for the quadratic case \(n = 2\). The main result of the presented work can be formulated as the following lower bounds \(C_l(n) \geq 6\) for \(n = 3\), \(C_l(n) \geq 10\) for \(n = 4\), \(C_l(n) \geq (n^2 + n - 2)/2\) for \(5 \leq n \leq 9\), \(C_l(n) \geq (n^2 + n - 4)/2\) for \(10 \leq n \leq 16\). The main technique for proving the above result is the study of perturbations of reversible holomorphic (isochronous) centers, inside the reversible centers class. More concretely, the authors study the Taylor developments of the period constants with respect to the perturbation parameters.
scientific article; zbMATH DE number 7361047
scientific article