Bifurcations of periodic solutions for plane mappings (Q1310371)

The authors investigate the Taylor mapping \[ F_ A: \begin{cases} x_ 1 = 2x-y+A\sin x\\y_ 1 = x\end{cases} \] for \(A\in (4,3/2\pi]\). They prove that for such \(F_ A\) there exists a regular homoclinic point. This implies the existence of infinitely many periodic points. Earlier, an analogous result for \(A\in (3/2 \pi,\infty)\) was obtained by Zhu Si-ming and others. Similar assertion for the mapping describing the motion of a bouncing ball is also true.