Continued Compositions of Linear Fractional Transformations
نویسندگان
چکیده
منابع مشابه
Contractivity of linear fractional transformations
One possible approach to exact real arithmetic is to use linear fractional transformations (LFT's) to represent real numbers and computations on real numbers. Recursive expressions built from LFT's are only convergent (i.e., denote a well-deened real number) if the involved LFT's are suuciently contractive. In this paper, we deene a notion of contrac-tivity for LFT's. It is used for convergence...
متن کاملOrphans in Forests of Linear Fractional Transformations
A positive linear fractional transformation (PLFT) is a function of the form f(z) = az+b cz+d where a, b, c and d are nonnegative integers with determinant ad− bc 6= 0. Nathanson generalized the notion of the Calkin-Wilf tree to PLFTs and used it to partition the set of PLFTs into an infinite forest of rooted trees. The roots of these PLFT Calkin-Wilf trees are called orphans. In this paper, we...
متن کاملDifferential Subordinations for Fractional- Linear Transformations
We establish that the differential subordinations of the forms p(z)+γzp′(z)≺ h(A1,B1;z) or p(z)+γzp′(z)/p(z) ≺ h(A2,B2;z) implies p(z) ≺ h(A,B;z), where γ ≥ 0 and h(A,B;z)= (1+Az)/(1+Bz) with −1≤ B <A.
متن کاملThe Theory of Linear Fractional Transformations of Rational Quadratics
A standard technique for solving the recursion xn+1 = g (xn) where g : C→ C is a complex function is to first find a fairly simple function g : C→ C and a bijection f : C→ C such that g = f◦g◦f−1 where ◦ is the composition of functions. Then xn = g (x0) = (f ◦ g ◦ f−1) (x0) where g and g are the n-fold composition of functions and g is fairly easy to compute. With this motivation we find all pa...
متن کاملA Theory of Linear Fractional Transformations of Rational Functions
If g, g are complex rational functions, we say that g ∼ g if g = ( ax+b cx+d )−1 ◦ g ◦ (ax+b cx+d ) , where ∣∣∣∣ a b c d ∣∣∣∣ 6= 0. For practical purposes, the general problem of finding a collection of rational invariants that are sufficient to partition ∼ into equivalency classes may be intractable for arbitrary degree rational functions. In this paper, we first outline a simple and naive met...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1996
ISSN: 0022-247X
DOI: 10.1006/jmaa.1996.0130