Sur certaines zones absorbantes et zones chaotiques d'un endomorphisme bidimensionnel. (On certain absorptive areas and chaotic areas of a two- dimensional endomorphism)
Let T be an \(R^ 2\)-endomorphism (x;y)\(\to (f(x,y,\lambda);g(x,y,\lambda))\), f, g being continuous and smooth functions of the real variables x, y and the real parameter \(\lambda\). The endomorphism T is supposed to be of the type with vanishing Jacobian on a curve of the (x,y) plane, the first rank consequent of which is called the first rank critical curve. Papers quoted in the bibliography have shown that critical curves of various ranks play a fundamental role for the determination of chaotic properties of T. In particular, these properties are related to the existence of absorptive areas, and chaotic areas, the boundaries of which are segments of such critical curves. This paper gives a practical method for the construction of these boundaries from three propositions proved for a well defined class of \(R^ 2\)- endomorphisms.
scientific article; zbMATH DE number 4015743