Let/(z) be a holomorph.self-map on C.-G-(0) with essential singularities 0 and It is proved that f(z) has a completdy invariant domain.D.F(f),then D is doubly connected and D contains all the singularities of the inv...Let/(z) be a holomorph.self-map on C.-G-(0) with essential singularities 0 and It is proved that f(z) has a completdy invariant domain.D.F(f),then D is doubly connected and D contains all the singularities of the inverse of f(z),moreover,if f is of the finite type, then D=F(f). This result implies that f(z) has at most one completely invariant domain in F(f).展开更多
Considering a family of rational maps Tnλconcerning renormalization transform ation,we give a perfect description about the dynamical properties of Tnλand the topological properties of the Fatou components F(Tnλ).F...Considering a family of rational maps Tnλconcerning renormalization transform ation,we give a perfect description about the dynamical properties of Tnλand the topological properties of the Fatou components F(Tnλ).Furthermore,we discuss the continuity of the Hausdorff dimension HD(J(Tnλ))about real param eter A.展开更多
文摘Let/(z) be a holomorph.self-map on C.-G-(0) with essential singularities 0 and It is proved that f(z) has a completdy invariant domain.D.F(f),then D is doubly connected and D contains all the singularities of the inverse of f(z),moreover,if f is of the finite type, then D=F(f). This result implies that f(z) has at most one completely invariant domain in F(f).
基金This work was supported by the National Natural Science Foundation of China(Grant No.11571049)the Special Basic Scientific Research Funds of Central Universities in China.
文摘Considering a family of rational maps Tnλconcerning renormalization transform ation,we give a perfect description about the dynamical properties of Tnλand the topological properties of the Fatou components F(Tnλ).Furthermore,we discuss the continuity of the Hausdorff dimension HD(J(Tnλ))about real param eter A.
