论文信息 - SOME CONTACT BIFURCATIONS IN TWO–DIMENSIONAL EXAMPLES

SOME CONTACT BIFURCATIONS IN TWO–DIMENSIONAL EXAMPLES

In this paper we consider some properties of two-dimensional noninvertible maps, which possess a chaotic attractor. Contact bifurcations causing a qualitative change in the shape of chaotic attractors, or causing their destabilization, have been considered in several papers since the early work in 1978 [19]. Such contact bifurcations, due to the contact between the boundary of a chaotic attracting set or area, and the boundary of its basin of attraction, may involve a fuzzy (or chaotic) basin boundary. In the examples considered in this paper we shall see that such bifurcations correspond to homoclinic bifurcations of repelling cycles of the map (repelling nodes, foci or saddles).

LAURA GARDINI | L. Gardini | DANIÈLE FOURNIER–PRUNARET

[1] Jack K. Hale,et al. Symbolic dynamics and nonlinear semiflows , 1986 .

[2] On the bifurcation between a chaotic area of T K and a chaotic area of T , 1985 .

[3] Laura Gardini. Some global bifurcations of two-dimensional endomorphisms by use of critical lines , 1992 .

[4] J. Yorke,et al. Period Three Implies Chaos , 1975 .

[5] F. R. Marotto. Snap-back repellers imply chaos in Rn , 1978 .

[6] L. P. Šil'nikov,et al. ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. II , 1972 .

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

[8] P. Holmes. Chaotic Dynamics , 1985, IEEE Power Engineering Review.

[9] S. Smale. Diffeomorphisms with Many Periodic Points , 1965 .

[10] Quelques propriétés des lignes critiques d'une récurrence du second ordre à inverse non unique. Détermination d'une zone absorbante , 1984 .

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

[12] George D. Birkhoff,et al. On the periodic motions of dynamical systems , 1927, Hamiltonian Dynamical Systems.

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

[15] L. P. Šil'nikov. ON A POINCARÉ-BIRKHOFF PROBLEM , 1967 .

[16] Bifurcations occurring in absorptive and chaotic areas , 1987 .