The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linea...

This paper describes the methodology to deal with the behavior of a dynamical system such as plant controllers in the framework of Temporal Logic. Many important concepts of the dynamical system like stability or observability are represented in this framework. As a reasoning method, we present an w -graph approach which enables us to represent the dynamical behavior of a given system, and an a...

Inflationary cosmologies, regarded as dynamical systems, have rather simple asymptotic behavior, insofar as the cosmic baldness principle holds. Nevertheless, in the early stages of an inflationary process, the dynamical behavior may be very complex. In this paper, we show how even a simple inflationary scenario, based on Linde’s “chaotic inflation” proposal, manifests nontrivial dynamical effe...

This paper presents an approach to defining distances between nonlinear and hybrid dynamical systems based on formal power series theory. The main idea is that the input-output behavior of a wide range of dynamical systems can be encoded by rational formal power series. Hence, a natural distance between dynamical systems is the distance between the formal power series encoding their input-outpu...