Renewal theorems and mixing for non Markov flows with infinite measure

We obtain results on mixing for a large class of (not necessarily Markov) infinite measure semiflows and flows. Erickson proved, amongst other things, a strong renewal theorem in the corresponding i.i.d. setting. Using operator renewal theory, we extend Erickson’s methods to the deterministic (i.e. non-i.i.d.) continuous time setting and obtain results on mixing as a consequence

Averaging and rates of averaging for uniform families of deterministic fast-slow skew product systems

We consider families of fast-slow skew product maps of the form xn+1=xn+ϵa(xn,yn,ϵ), yn+1=Tϵyn, where Tϵ is a family of nonuniformly expanding maps, and prove averaging and rates of averaging for the slow variables x as ϵ→0. Similar results are obtained also for continuous time systems x˙=ϵa(x,y,ϵ), y˙=gϵ(y). Our results include cases where the family of fast dynamical systems consists of intermittent maps, unimodal maps (along the Collet–Eckmann parameters) and Viana maps

Boundedness, global existence and continuous dependence for nonlinear dynamical systems describing physiologically structured populations

Abstract The paper is aimed as a contribution to the general theory of nonlinear infinite dimensional dynamical systems describing interacting physiologically structured populations. We carry out continuation of local solutions to maximal solutions in a functional analytic setting. For maximal solutions we establish global existence via exponential boundedness and by a contraction argument, adapted to derive uniform existence time. Moreover, within the setting of dual Banach spaces, we derive results on continuous dependence with respect to time and initial state. To achieve generality the paper is organized top down, in the way that we first treat abstract nonlinear dynamical systems under very few but rather strong hypotheses and thereafter work our way down towards verifiable assumptions in terms of more basic biological modelling ingredients that guarantee that the high level hypotheses hold

Mathematical foundations of elasticity

[Preface] This book treats parts of the mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is intended for mathematicians, engineers, and physicists who wish to see this classical subject in a modern setting and to see some examples of what newer mathematical tools have to contribute

Advances in Robotics, Automation and Control

The book presents an excellent overview of the recent developments in the different areas of Robotics, Automation and Control. Through its 24 chapters, this book presents topics related to control and robot design; it also introduces new mathematical tools and techniques devoted to improve the system modeling and control. An important point is the use of rational agents and heuristic techniques to cope with the computational complexity required for controlling complex systems. Through this book, we also find navigation and vision algorithms, automatic handwritten comprehension and speech recognition systems that will be included in the next generation of productive systems developed by man