Geometric series with randomly increasing exponents

Geometric Exponents and Kleinian Groups

Formal power series with cyclically ordered exponents

We define and study a notion of ring of formal power series with exponents in a cyclically ordered group. Such a ring is a quotient of various subrings of classical formal power series rings. It carries a two variable valuation function. In the particular case where the cyclically ordered group is actually totally ordered, our notion of formal power series is equivalent to the classical one in ...

Lyapunov Exponents and Localization in Randomly Layered Media

are composed of a disordered or random collection of homogeneous layers. As an example, consider the model A variety of problems involving disordered systems can be formulated mathematically in terms of products of random transfer matrishown in Fig. 1. Here we have chosen a pseudo-random ces, including Ising spin systems, optical and continuum mechanical sequence (to be described later) of laye...

A Geometric Study of the Hypergeometric Function with Imaginary Exponents

CONTENTS The Schwarz map defined by the ratio of two solutions of the

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...