论文信息 - The Dynamics of Planar Quadratic Maps with Nonempty Bounded Critical Set

The Dynamics of Planar Quadratic Maps with Nonempty Bounded Critical Set

If the critical set of a planar quadratic map is bounded and nonempty, then the range is doubly covered except the image of the critical set and the region bounded by it (Fig. 1). For a map of this type, we showed that infinity is a sink and the set of bounded orbits is nonempty hence its boundary may be regarded as a generalization of Julia sets of complex quadratic maps. In this paper, we also provided evidences to conjecture that maps of this type have infinitely many periodic points.

Chia-Hsing Nien

[1] Laura Gardini,et al. Homoclinic bifurcations in n -dimensional endomorphisms, due to expanding periodic points , 1994 .

[2] C. Mira,et al. Complex dynamics in two-dimensional endomorphisms , 1980 .

[3] Shmuel Friedland,et al. Dynamical properties of plane polynomial automorphisms , 1989, Ergodic Theory and Dynamical Systems.

[4] S. Wang. A Jacobian criterion for separability , 1980 .

[5] Christian Mira,et al. On Some Properties of Invariant Sets of Two-Dimensional Noninvertible Maps , 1997 .

[6] FRACTAL AGGREGATION OF BASIN ISLANDS IN TWO-DIMENSIONAL QUADRATIC NONINVERTIBLE MAPS , 1995 .

[7] Jürgen Moser,et al. On quadratic symplectic mappings , 1994 .

[8] H. Bass,et al. The Jacobian conjecture: Reduction of degree and formal expansion of the inverse , 1982 .

[9] M. Fried,et al. On the Jacobian conjecture and the configurations of roots. , 1983 .

[10] Christian Mira,et al. ON BEHAVIORS OF TWO-DIMENSIONAL ENDOMORPHISMS: ROLE OF THE CRITICAL CURVES , 1993 .

[11] Raymond A. Adomaitis,et al. Noninvertibility and the structure of basins of attraction in a model adaptive control system , 1991 .

[12] Christian Mira,et al. Basin bifurcations of two-dimensional noninvertible maps : Fractalization of basins , 1994 .