Mae pump ffrind 12-13 oed wedi cael eu noddi i aros mewn hen blasdy am un noson. Oes ¿na ysbryd yn cuddio yno?Five friends have been sponsored to spend the night in a haunted mansion.

An authoritative treatment by leading researchers covering theory and optimal estimation, along with practical applications.

This book looks at dynamics as an iteration process where the output of a function is fed back as an input to determine the evolution of an initial state over time. The theory examines errors which arise from round-off in numerical simulations, from the inexactness of mathematical models used to describe physical processes, and from the effects of external controls. The author provides an introduction accessible to beginning graduate students and emphasizing geometric aspects of the theory. Conley's ideas about rough orbits and chain-recurrence play a central role in the treatment. The book will be a useful reference for mathematicians, scientists, and engineers studying this field, and an ideal text for graduate courses in dynamical systems.

Fluids that mix at geophysical or microscales tend to form well-mixed areas and regions of coherent blobs. The Antarctic circumpolar vortex, which mostly retains its structure while moving unsteadily in the atmosphere, is an example of a coherent structure. How do such structures exchange fluid with their surroundings? What is the impact on global mixing? What is the "boundary" of the structure, and how does it move? Can these questions be answered from time-varying observational data? This book addresses these issues from the perspective of the differential equations that must be obeyed by fluid particles. In these terms, identification of the boundaries of coherent structures (i.e., "flow barriers"), quantification of transport across them, control of the locations of these barriers, and optimization of transport across them are developed using a rigorous mathematical framework. The concepts are illustrated with an array of theoretical and applied examples that arise from oceanography and microfluidics. Barriers and Transport in Unsteady Flows: A Melnikov Approach provides an extensive introduction and bibliography, specifically elucidating the difficulties arising when flows are unsteady and highlighting relevance in geophysics and microfluidics; careful and rigorous development of the mathematical theory of unsteady flow barriers within the context of nonautonomous stable and unstable manifolds, richly complemented with examples; and chapters on exciting new research in the control of flow barriers and the optimization of transport across them.

An extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurcation problems arising for ordinary differential equations in one- and two-dimensions, this book describes several tools from the theory of infinite dimensional dynamical systems, allowing the reader to treat more complicated bifurcation problems, such as bifurcations arising in partial differential equations. Attention is restricted to the study of local bifurcations with a focus upon the center manifold reduction and the normal form theory; two methods that have been widely used during the last decades. Through use of step-by-step examples and exercises, a number of possible applications are illustrated, and allow the less familiar reader to use this reduction method by checking some clear assumptions. Written by recognised experts in the field of center manifold and normal form theory this book provides a much-needed graduate level text on bifurcation theory, center manifolds and normal form theory. It will appeal to graduate students and researchers working in dynamical system theory.

No detailed description available for "Proceedings of the seventh International Colloquium on Differential Equations".

Based on a one-year course taught by the author to graduates at the University of Missouri, this book provides a student-friendly account of some of the standard topics encountered in an introductory course of ordinary differential equations. In a second semester, these ideas can be expanded by introducing more advanced concepts and applications. A central theme in the book is the use of Implicit Function Theorem, while the latter sections of the book introduce the basic ideas of perturbation theory as applications of this Theorem. The book also contains material differing from standard treatments, for example, the Fiber Contraction Principle is used to prove the smoothness of functions that are obtained as fixed points of contractions. The ideas introduced in this section can be extended to infinite dimensions.

This thesis deals with the dynamics of state-of-the-art nanophotonic semiconductor structures, providing essential information on fundamental aspects of nonlinear dynamical systems on the one hand, and technological applications in modern telecommunication on the other. Three different complex laser structures are considered in detail: (i) a quantum-dot-based semiconductor laser under optical injection from a master laser, (ii) a quantum-dot laser with optical feedback from an external resonator, and (iii) a passively mode-locked quantum-well semiconductor laser with saturable absorber under optical feedback from an external resonator. Using a broad spectrum of methods, both numerical and analytical, this work achieves new fundamental insights into the interplay of microscopically based nonlinear laser dynamics and optical perturbations by delayed feedback and injection.

In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.