Sentence examples for be a hyperbolic polynomial from inspiring English sources

Let p be a hyperbolic polynomial with connected Julia set.

Moreover, the map σ has the following expansion with respect to the parameter a (see Lemma 12.2 in [9]): sigma t,z) = biggl dt, agamma(t) -frac{a^{2}z}{p'(gamma (t))}+mathcal{O} bigl(a^{3}bigr) biggr), where γ is the Carathéodory loop of the polynomial p. Let p be a hyperbolic polynomial with connected Julia set.

Let us consider the r-jet of g at such a point: begin{aligned} g_{(x,upxi )} (y,upeta )mathrel {mathop :}=sum _{alpha,beta :|alpha |+|beta |<r} frac{1}{alpha !beta !} g^{(alpha )}_{(beta )}(x,upxi ) y^beta upeta ^alpha ; end{aligned} (2.37 it is a hyperbolic polynomial with respect to (eta _0).

Let ((M,d)) be a hyperbolic metric space.

Let ((X,d)) be a hyperbolic metric space.

Let q be a hyperbolic periodic point of f.

Definition 3.3 Let ( M, d ) be a hyperbolic metric space.

Let X be a hyperbolic ordered metric space.

Let p be a hyperbolic periodic point of f.

With such a model, there may be a hyperbolic perception of pigmentation in darker-skinned women.

We give a new proof of a theorem of Hubbard and Oberste-Vorth (Real and Complex Dynamical Systems, pp. 89-132, 1995) for Hénon maps that are perturbations of a hyperbolic polynomial and obtain the Julia set (J^) inside a polydisk as the image of the fixed point of a contracting operator.