A Characterization of Möbius Transformations

Möbius Iterated Function Systems

Iterated function systems have been most extensively studied when the functions are affine transformations of Euclidean space and, more recently, projective transformations on real projective space. This paper investigates iterated function systems consisting of Möbius transformations on the extended complex plane or, equivalently, on the Riemann sphere. The main result is a characterization, i...

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles

Involutions on a group of Möbius transformations 1 Möbius transformations

certain restrictions on the entries of A such that ψ(x) = (ax+ b)(cx+ d)−1, x ∈ Rn, and cx+ d 6= 0. Let O(n) be the real orthogonal group, i.e., the group of invertible linear transformations of Rn that preserve the inner-product K. For any v ∈ Rn, let v⊥ = {x ∈ Rn : K(x, v) = 0}, span(v) = {αv : α ∈ R}, and let ‖v‖ = K(v, v)1/2 be the Euclidean norm. Suppose v is a unit vector, i.e., ‖v‖ = 1. ...

Conjugacy Classification of Quaternionic Möbius Transformations

It is well known that the dynamics and conjugacy class of a complex Möbius transformation can be determined from a simple rational function of the coefficients of the transformation. We study the group of quaternionic Möbius transformations and identify simple rational functions of the coefficients of the transformations that determine dynamics and conjugacy.

A Characterization of the Entropy--Gibbs Transformations

Let h be a finite dimensional complex Hilbert space, b(h)+ be the set of all positive semi-definite operators on h and Phi is a (not necessarily linear) unital map of B(H) + preserving the Entropy-Gibbs transformation. Then there exists either a unitary or an anti-unitary operator U on H such that Phi(A) = UAU* for any B(H) +. Thermodynamics, a branch of physics that is concerned with the study...