### For REFEREES

 On the $F$-expanding of Homoclinic classes Wanlou WU,Bo LI Keywords:Homoclinic classes, Thin trapped, Periodic points, Uniformly expanding Abstract: We establish a closing property for thin trapped (see Definition \ref{Def:TP}) homoclinic classes. Taking advantage of this property, we prove that if a homoclinic class $H(f, p)$ admits a dominated splitting \$T_{H(f, p)}M=E\oplus_