Resonances are ubiquitous in dynamical systems with many degrees of freedom. They have the basic effect of introducing slow-fast behavior in an evolutionary system which, coupled with instabilities, can result in highly irregular behavior. This book gives a unified treatment of resonant problems with special emphasis on the recently discovered phenomenon of homoclinic jumping. After a survey of the necessary background, a general finite dimensional theory of homoclinic jumping is developed and illustrated with examples. The main mechanism of chaos near resonances is discussed in both the dissipative and the Hamiltonian context. Previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds are described. The results are applied to a variety of different problems, which include applications from beam oscillations, surface wave dynamics, nonlinear optics, atmospheric science and fluid mechanics. The theory is further used to study resonances in Hamiltonian systems with applications to molecular dynamics and rigid body motion. The final chapter contains an infinite dimensional extension of the finite dimensional theory, with application to the perturbed nonlinear Schrodinger equation and coupled NLS equations."

In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscillators, geometric singular perturbation theory, and the study of bursting phenomena in biological oscillators. "Invariant manifold theorems" have become standard tools for applied mathematicians, physicists, engineers, and virtually anyone working on nonlinear problems from a geometric viewpoint. In this book, the author gives a self-contained development of these ideas as well as proofs of the main theorems along the lines of the seminal works of Fenichel. In general, the Fenichel theory is very valuable for many applications, but it is not easy for people to get into from existing literature. This book provides an excellent avenue to that. Wiggins also describes a variety of settings where these techniques can be used in applications.

In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscillators, geometric singular perturbation theory, and the study of bursting phenomena in biological oscillators. "Invariant manifold theorems" have become standard tools for applied mathematicians, physicists, engineers, and virtually anyone working on nonlinear problems from a geometric viewpoint. In this book, the author gives a self-contained development of these ideas as well as proofs of the main theorems along the lines of the seminal works of Fenichel. In general, the Fenichel theory is very valuable for many applications, but it is not easy for people to get into from existing literature. This book provides an excellent avenue to that. Wiggins also describes a variety of settings where these techniques can be used in applications.

A unified treatment of resonant problems with special emphasis on the recently discovered phenomenon of homoclinic jumping. After a survey of the necessary background, the book develops a general finite dimensional theory of homoclinic jumping, illustrating it with examples. The main mechanism of chaos near resonances is discussed in both the dissipative and the Hamiltonian context, incorporating previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds. The results are applied to a variety of different problems, which include applications from beam oscillations, surface wave dynamics, nonlinear optics, atmospheric science and fluid mechanics.

Now in paperback, the Oxford Textbook of Oncology reflects current best practice in the multidisciplinary management of cancer, written and edited by internationally recognised leaders in the field. Structured in six sections, the book provides an accessible scientific basis to the key topics of oncology, examining how cancer cells grow and function, as well as discussing the aetiology of cancer, and the general principles governing modern approaches to oncology treatment. The book examines the challenges presented by the treatment of cancer on a larger scale within population groups, and the importance of recognising and supporting the needs of individual patients, both during and after treatment. A series of disease-oriented, case-based chapters, ranging from acute leukaemia to colon cancer, highlight the various approaches available for managing the cancer patient, including the translational application of cancer science in order to personalise treatment. The advice imparted in these cases has relevance worldwide, and reflects a modern approach to cancer care. The Oxford Textbook of Oncology provides a comprehensive account of the multiple aspects of best practice in the discipline, making it an indispensable resource for oncologists of all grades and subspecialty interests.

Written and edited by internationally recognised leaders in the field, the new edition of the Oxford Textbook of Oncology has been fully revised and updated, taking into consideration the advancements in each of the major therapeutic areas, and representing the multidisciplinary management of cancer. Structured in six sections, the book provides an accessible scientific basis to the key topics of oncology, examining how cancer cells grow and function, as well as discussing the aetiology of cancer, and the general principles governing modern approaches to oncology treatment. The book examines the challenges presented by the treatment of cancer on a larger scale within population groups, and the importance of recognising and supporting the needs of individual patients, both during and after treatment. A series of disease-oriented, case-based chapters, ranging from acute leukaemia to colon cancer, highlight the various approaches available for managing the cancer patient, including the translational application of cancer science in order to personalise treatment. The advice imparted in these cases has relevance worldwide, and reflects a modern approach to cancer care. The Oxford Textbook of Oncology provides a comprehensive account of the multiple aspects of best practice in the discipline, making it an indispensable resource for oncologists of all grades and subspecialty interests.