Kategoria BISAC: Mathematics >> Differential Equations - General

This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are...

Using phase plane analysis, findings from the theory of topological horseshoes and linked-twist maps, this book presents a novel method to prove the existence of chaotic dynamics. Indynamical systems, complex behavior in amap can be indicated by showingthe existence of a Smale-horseshoe-like structure, either for the map itself or its iterates. This usually requires some assumptions about the map, such as a diffeomorphism and some hyperbolicity conditions. In this text, less stringent definitions of a horseshoe have been suggested so as to reproduce somegeometrical features typical of the...

This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales. Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics or researchers seeking a no-nonsense approach, it discusses examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods.

The problems considered are given by singular perturbed reaction...

This volume contains extended abstracts outlining selected talks and other selected presentations given by participants throughout the -Intensive Research Program on Advances in Nonsmooth Dynamics 2016-, held at the Centre de Recerca Matematica (CRM) in Barcelona from February 1st to April 29th, 2016. They include brief research articles reporting new results, descriptions of preliminary work or open problems, and outlines of prominent discussion sessions. The articles are all the result of direct collaborations initiated during the research program.

The topic is the theory and...