The existence of homoclinic orbits to saddle-focus (Q1774869)

The authors deal with the existence of homoclinic orbits to saddle-focus. To this end they present an improved version of the existence criterion for such homoclinic orbits to saddle-focus. Based on this criterion, the authors correct the result of \textit{T. Zhou}, \textit{G. Chen} and \textit{Q. Yang} [Chaos Solitons Fractals 19, 985--993 (2004; Zbl 1053.37015)]. Moreover, the authors show that the method presented in this paper easily leads to nonexistence of horseshoe chaos in the sense of Silnikov.