Invariant graphs of a family of non-uniformly expanding skew products over Markov maps

We consider a family of skew-products of the form $(Tx, g_x(t)) : X \times \mathbb{R} \to X \times \mathbb{R}$ where $T$ is a continuous expanding Markov map and $g_x : \mathbb{R} \to \mathbb{R}$ is a family of homeomorphisms of $\mathbb{R}$. A function $u: X \to \mathbb{R}$ is said to be an invariant graph if $\mathrm{graph}(u) = \{(x,u(x)) \mid x\in X\}$ is an invariant set for the skew-product; equivalently if $u(T(x)) = g_x(u(x))$. A well-studied problem is to consider the existence, regularity and dimension-theoretic properties of such functions, usually under strong contraction or expansion conditions (in terms of Lyapunov exponents or partial hyperbolicity) in the fibre direction. Here we consider such problems in a setting where the Lyapunov exponent in the fibre direction is zero on a set of periodic orbits. We prove that $u$ either has the structure of a `quasi-graph' (or `bony graph') or is as smooth as the dynamics, and we give a criteria for this to happen.Comment: 21 pages, 2 figure

Boss Lady: How Female Chinese Managers Succeed in China's Guanxi System

This project examines how female Chinese managers within China’s traditionally male-dominated, guanxi-related private sector are coming into their own as leaders of the new Chinese economy. In this project, guanxi (关系) is defined as “interpersonal relations and connections” and research hinges around investigating how female Chinese managers use, or do not use, guanxi in their careers and personal lives. After establishing a background of preexisting scholarship, this project implements a Case Study Analysis chapter on three “self made” female entrepreneurs followed by an “Interview Analysis” chapter conducted with four female managers that took place in May, 2014. The goal of these two chapters is to find what common factors influenced three female entrepreneurs to achieve success and then apply these findings via four hypotheses to the Interview Analysis portion. In this way, research examines the personal stories of four female Chinese managers as well as a more traditional Case Study analysis of three wildly successful female entrepreneurs. The combination of a case study analysis combined with a series of interviews is rare in this field as preexisting scholarship pertaining to how women interact with China’s traditional guanxi-dependent corporate culture is rare. This project discovers how female Chinese managers are building their own female-centric guanxi networks as well as implementing new managerial strategies to safeguard their newfound positions of power. At the conclusion of this project, a new trend of female-led guanxi networks emerges as well as how women are now becoming power-players within China’s private sector