In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

Seeking exactness for \convex relaxation", we deene a map f : < n ! < m to be ICON if its image f(< n) is convex. Analogously, f is termed LICON(AICON) if the image of every linear (every aane) vsubspace under f is convex. In this paper, we investigate quadratic maps of these three types. These maps are motivated by a fact shown here that they prescribe conditions under which feasibility and op...

The renormalization of a quadratic-like map is studied. The threedimensional Yoccoz puzzle for an infinitely renormalizable quadratic-like map is discussed. For an unbranched quadratic-like map having the a priori complex bounds, the local connectivity of its Julia set is proved by using the three-dimensional Yoccoz puzzle. The generalized version of Sullivan’s sector theorem is discussed and i...

Consider an analytic map from a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of vector lines to germs of circles. Such map is called rounding. Two roundings are equivalent if they take the same lines to the same circles. We prove that any rounding whose differential at 0 has rank at least 2 is equivalent to a fractional quadratic rounding. The ...

The global superstability of a dynamical system is allowed when all bounded orbits of this system are superstable, .i.e. There exist a minus infinity Lyapunouv exponent. In this paper it is shown that any globally superstable 2-D quadratic map is conjugate to the 1D quadratic map. This result allow us to determine some forms of superstable 1-D quadratic maps.

We study the class of entire transcendental maps of finite order with one critical point and one asymptotic value, which has exactly one finite pre-image, and having a persistent Siegel disc. After normalisation this is a one parameter family fa with a ∈ C ∗ which includes the semi-standard map λzez at a = 1, approaches the exponential map when a → 0 and a quadratic polynomial when a → ∞. We in...