Homogenization on arbitrary manifolds

We describe a setting for homogenization of convex hamiltonians on abelian covers of any compact manifold. In this context we also provide a simple variational proof of standard homogenization results.Comment: 17 pages, 1 figur

Topological Shocks in Burgers Turbulence

The dynamics of the multi-dimensional randomly forced Burgers equation is studied in the limit of vanishing viscosity. It is shown both theoretically and numerically that the shocks have a universal global structure which is determined by the topology of the configuration space. This structure is shown to be particularly rigid for the case of periodic boundary conditions.Comment: 4 pages, 4 figures, RevTex4, published versio

On the negative relation between investment-cash flow sensitivities and cash-cash flow.

We predict and find empirical support for a negative relation between the firm’s investment-cash flow sensitivity and cash-cash flow sensitivity, two measures suggested to capture the concept of financing constraints. This negative relation on the firm-level stems from the fact that both investments and the cash account are uses of funds competing for limited available cash flows. Additionally, we find that the investment-cash flow sensitivity is a better predictor for the firm’s constraint-status than the cash-cash flow sensitivity for a longitudinal sample of 1,233 U.S.-based listed firms using an evaluative framework based upon ex-post evaluation of the firmvarying sensitivities.financing constraints; investment-cash flow sensitivities; cash-cash flow sensitivities; firm-varying sensitivities;

Convergence of the solutions of the discounted equation

We consider a continuous coercive Hamiltonian $H$ on the cotangent bundle of the compact connected manifold $M$ which is convex in the momentum. If $u_\lambda:M\to\mathbb R$ is the viscosity solution of the discounted equation $$\lambda u_\lambda(x)+H(x,d_x u_\lambda)=c(H),$$ where $c(H)$ is the critical value, we prove that $u_\lambda$ converges uniformly, as $\lambda\to 0$, to a specific solution $u_0:M\to\mathbb R$ of the critical equation $$H(x,d_x u)=c(H).$$ We characterize $u_0$ in terms of Peierls barrier and projected Mather measures.Comment: 35 page