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Differential Equations and Dynamical Systems
This volume contains contributed papers authored by participants of a Conference on Differential Equations and Dynamical Systems which was held at the Instituto Superior Tecnico (Lisbon, Portugal). The conference brought together a large number of specialists in the area of differential equations and dynamical systems and provided an opportunity to celebrate Professor Waldyr Oliva's 70th birthday, honoring his fundamental contributions to the field. The volume constitutes anoverview of the current research over a wide range of topics, extending from qualitative theory for (ordinary, partial or functional) differential equations to hyperbolic dynamics and ergodic theory.
Partial Differential Equations and Functional Analysis
Mark Vishik was one of the prominent figures in the theory of partial differential equations. His ground-breaking contributions were instrumental in integrating the methods of functional analysis into this theory. The book is based on the memoirs of his friends and students, as well as on the recollections of Mark Vishik himself, and contains a detailed description of his biography: childhood in Lwów, his connections with the famous Lwów school of Stefan Banach, a difficult several year long journey from Lwów to Tbilisi after the Nazi assault in June 1941, going to Moscow and forming his own school of differential equations, whose central role was played by the famous Vishik Seminar at th...
Patterns of Dynamics
Theoretical advances in dynamical-systems theory and their applications to pattern-forming processes in the sciences and engineering are discussed in this volume that resulted from the conference Patterns in Dynamics held in honor of Bernold Fiedler, in Berlin, July 25-29, 2016.The contributions build and develop mathematical techniques, and use mathematical approaches for prediction and control of complex systems. The underlying mathematical theories help extract structures from experimental observations and, conversely, shed light on the formation, dynamics, and control of spatio-temporal patterns in applications. Theoretical areas covered include geometric analysis, spatial dynamics, spectral theory, traveling-wave theory, and topological data analysis; also discussed are their applications to chemotaxis, self-organization at interfaces, neuroscience, and transport processes.
Trends in Nonlinear Analysis
Applied mathematics is a central connecting link between scientific observations and their theoretical interpretation. Nonlinear analysis has surely contributed major developments which nowadays shape the face of applied mathematics. At the beginning of the millennium, all sciences are expanding at increased speed. Technological, ecological, economical and medical problem solving is a central issue of every modern society. Mathematical models help to expose fundamental structures hidden in these problems and serve as unifying tools to deepen our understanding. What are the new challenges applied mathematics has to face with the increased diversity of scientific problems? In which direction should the classical tools of nonlinear analysis be developed further? How do new available technologies influence the development of the field? How can problems be solved which have been beyond reach in former times? It is the aim of this book to explore new developments in the field by way of discussion of selected topics from nonlinear analysis.
Space – Time – Matter
This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian mani...
Annals of Mathematics Studies
"Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B. H. Neumann introduced this system in the 1950s, and J. Moser popularized it as a toy model for celestial mechanics. All along, the so-called Moser-Neumann question has been one of the central problems in the field. This question asks whether or not one can have an outer billiards system with an unbounded orbit. The Moser-Neumann question is an idealized version of the question of whether, because of small disturbances in its orbit, the Earth can break out of its orbit and fly away from the Sun. In Outer Billiards on Kites, Richard Schwartz presents his affirmative solution to the Moser-Neumann pr...
Nonlinear Dynamics
This book, which presents results in nonlinear dynamical systems from the physical and engineering sciences, has a fractal-like construction: Each of the 17 chapters reviews the present status of research activities from the field under consideration, first by providing the reader with an elementary introduction to the topic, then presenting the latest concepts, and finally introducing theoretical, computational or experimental results. The general construction of the book is also presented in a similar manner - starting with the outline of new theoretical achievements and finishing with various problems relevant to the fields of electrical and electronics engineering, mechanical engineering and biomechanical engineering. The new aspects and results found in the special systems taken from electrical, mechanical and biomechanical engineering enrich and increase the general level of understanding the dynamical behaviour of physical systems and show many of their universal properties.
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