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This book is aimed at mathematicians, scientists, and engineers,
studying models that involve a discontinuity, or studying the
theory of nonsmooth systems for its own sake. It is divided in two
complementary courses: piecewise smooth flows and maps,
respectively. Starting from well known theoretical results, the
authors bring the reader into the latest challenges in the field,
going through stability analysis, bifurcation, singularities,
decomposition theorems and an introduction to kneading theory. Both
courses contain many examples which illustrate the theoretical
concepts that are introduced.
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
applications of Nonsmooth Dynamics. This includes systems involving
elements of: impacting, switching, on/off control, hybrid
discrete-continuous dynamics, jumps in physical properties, and
many others. Applications include: electronics, climate modeling,
life sciences, mechanics, ecology, and more. Numerous new results
are reported concerning the dimensionality and robustness of
nonsmooth models, shadowing variables, numbers of limit cycles,
discontinuity-induced bifurcations and chaos, determinacy-breaking,
stability criteria, and the classification of attractors and other
singularities. This material offers a variety of new exciting
problems to mathematicians, but also a diverse range of new tools
and insights for scientists and engineers making use of
mathematical modeling and analysis. The book is intended for
established researchers, as well as for PhD and postdoctoral
students who want to learn more about the latest advances in these
highly active areas of research.
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